{"id":13952,"date":"2022-05-09T13:47:10","date_gmt":"2022-05-09T11:47:10","guid":{"rendered":"https:\/\/college-willy-ronis.fr\/maths\/?p=13952"},"modified":"2026-04-17T06:37:05","modified_gmt":"2026-04-17T04:37:05","slug":"chapitre-19-somme-des-mesures-des-angles-dun-triangle","status":"publish","type":"post","link":"https:\/\/college-willy-ronis.fr\/maths\/chapitre-19-somme-des-mesures-des-angles-dun-triangle\/","title":{"rendered":"Chapitre 19 : Somme des mesures des angles d&rsquo;un triangle"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"13952\" class=\"elementor elementor-13952\">\n\t\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-21577810 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"21577810\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;gradient&quot;,&quot;shape_divider_bottom&quot;:&quot;wave-brush&quot;}\">\n\t\t\t\t\t\t\t<div class=\"elementor-background-overlay\"><\/div>\n\t\t\t\t\t\t<div class=\"elementor-shape elementor-shape-bottom\" data-negative=\"false\">\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 283.5 27.8\" preserveAspectRatio=\"none\">\n\t<path class=\"elementor-shape-fill\" d=\"M283.5,9.7c0,0-7.3,4.3-14,4.6c-6.8,0.3-12.6,0-20.9-1.5c-11.3-2-33.1-10.1-44.7-5.7\ts-12.1,4.6-18,7.4c-6.6,3.2-20,9.6-36.6,9.3C131.6,23.5,99.5,7.2,86.3,8c-1.4,0.1-6.6,0.8-10.5,2c-3.8,1.2-9.4,3.8-17,4.7\tc-3.2,0.4-8.3,1.1-14.2,0.9c-1.5-0.1-6.3-0.4-12-1.6c-5.7-1.2-11-3.1-15.8-3.7C6.5,9.2,0,10.8,0,10.8V0h283.5V9.7z M260.8,11.3\tc-0.7-1-2-0.4-4.3-0.4c-2.3,0-6.1-1.2-5.8-1.1c0.3,0.1,3.1,1.5,6,1.9C259.7,12.2,261.4,12.3,260.8,11.3z M242.4,8.6\tc0,0-2.4-0.2-5.6-0.9c-3.2-0.8-10.3-2.8-15.1-3.5c-8.2-1.1-15.8,0-15.1,0.1c0.8,0.1,9.6-0.6,17.6,1.1c3.3,0.7,9.3,2.2,12.4,2.7\tC239.9,8.7,242.4,8.6,242.4,8.6z M185.2,8.5c1.7-0.7-13.3,4.7-18.5,6.1c-2.1,0.6-6.2,1.6-10,2c-3.9,0.4-8.9,0.4-8.8,0.5\tc0,0.2,5.8,0.8,11.2,0c5.4-0.8,5.2-1.1,7.6-1.6C170.5,14.7,183.5,9.2,185.2,8.5z M199.1,6.9c0.2,0-0.8-0.4-4.8,1.1\tc-4,1.5-6.7,3.5-6.9,3.7c-0.2,0.1,3.5-1.8,6.6-3C197,7.5,199,6.9,199.1,6.9z M283,6c-0.1,0.1-1.9,1.1-4.8,2.5s-6.9,2.8-6.7,2.7\tc0.2,0,3.5-0.6,7.4-2.5C282.8,6.8,283.1,5.9,283,6z M31.3,11.6c0.1-0.2-1.9-0.2-4.5-1.2s-5.4-1.6-7.8-2C15,7.6,7.3,8.5,7.7,8.6\tC8,8.7,15.9,8.3,20.2,9.3c2.2,0.5,2.4,0.5,5.7,1.6S31.2,11.9,31.3,11.6z M73,9.2c0.4-0.1,3.5-1.6,8.4-2.6c4.9-1.1,8.9-0.5,8.9-0.8\tc0-0.3-1-0.9-6.2-0.3S72.6,9.3,73,9.2z M71.6,6.7C71.8,6.8,75,5.4,77.3,5c2.3-0.3,1.9-0.5,1.9-0.6c0-0.1-1.1-0.2-2.7,0.2\tC74.8,5.1,71.4,6.6,71.6,6.7z M93.6,4.4c0.1,0.2,3.5,0.8,5.6,1.8c2.1,1,1.8,0.6,1.9,0.5c0.1-0.1-0.8-0.8-2.4-1.3\tC97.1,4.8,93.5,4.2,93.6,4.4z M65.4,11.1c-0.1,0.3,0.3,0.5,1.9-0.2s2.6-1.3,2.2-1.2s-0.9,0.4-2.5,0.8C65.3,10.9,65.5,10.8,65.4,11.1\tz M34.5,12.4c-0.2,0,2.1,0.8,3.3,0.9c1.2,0.1,2,0.1,2-0.2c0-0.3-0.1-0.5-1.6-0.4C36.6,12.8,34.7,12.4,34.5,12.4z M152.2,21.1\tc-0.1,0.1-2.4-0.3-7.5-0.3c-5,0-13.6-2.4-17.2-3.5c-3.6-1.1,10,3.9,16.5,4.1C150.5,21.6,152.3,21,152.2,21.1z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M269.6,18c-0.1-0.1-4.6,0.3-7.2,0c-7.3-0.7-17-3.2-16.6-2.9c0.4,0.3,13.7,3.1,17,3.3\tC267.7,18.8,269.7,18,269.6,18z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M227.4,9.8c-0.2-0.1-4.5-1-9.5-1.2c-5-0.2-12.7,0.6-12.3,0.5c0.3-0.1,5.9-1.8,13.3-1.2\tS227.6,9.9,227.4,9.8z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M204.5,13.4c-0.1-0.1,2-1,3.2-1.1c1.2-0.1,2,0,2,0.3c0,0.3-0.1,0.5-1.6,0.4\tC206.4,12.9,204.6,13.5,204.5,13.4z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M201,10.6c0-0.1-4.4,1.2-6.3,2.2c-1.9,0.9-6.2,3.1-6.1,3.1c0.1,0.1,4.2-1.6,6.3-2.6\tS201,10.7,201,10.6z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M154.5,26.7c-0.1-0.1-4.6,0.3-7.2,0c-7.3-0.7-17-3.2-16.6-2.9c0.4,0.3,13.7,3.1,17,3.3\tC152.6,27.5,154.6,26.8,154.5,26.7z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M41.9,19.3c0,0,1.2-0.3,2.9-0.1c1.7,0.2,5.8,0.9,8.2,0.7c4.2-0.4,7.4-2.7,7-2.6\tc-0.4,0-4.3,2.2-8.6,1.9c-1.8-0.1-5.1-0.5-6.7-0.4S41.9,19.3,41.9,19.3z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M75.5,12.6c0.2,0.1,2-0.8,4.3-1.1c2.3-0.2,2.1-0.3,2.1-0.5c0-0.1-1.8-0.4-3.4,0\tC76.9,11.5,75.3,12.5,75.5,12.6z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M15.6,13.2c0-0.1,4.3,0,6.7,0.5c2.4,0.5,5,1.9,5,2c0,0.1-2.7-0.8-5.1-1.4\tC19.9,13.7,15.7,13.3,15.6,13.2z\"\/>\n<\/svg>\t\t<\/div>\n\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-53ceeede\" data-id=\"53ceeede\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7215f41c elementor-widget elementor-widget-heading\" data-id=\"7215f41c\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Chapitre 19<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-20a1137f elementor-widget elementor-widget-heading\" data-id=\"20a1137f\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">Angles dans un triangle<\/h1>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ddc62a8 elementor-widget elementor-widget-text-editor\" data-id=\"ddc62a8\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-58ab6916\" data-id=\"58ab6916\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-49c8a268 elementor-widget elementor-widget-image\" data-id=\"49c8a268\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"300\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2020\/10\/labyrinthe-scratch-300x300.png\" class=\"attachment-medium size-medium wp-image-10183\" alt=\"cours de 5\u00e8me\" srcset=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2020\/10\/labyrinthe-scratch-300x300.png 300w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2020\/10\/labyrinthe-scratch-150x150.png 150w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2020\/10\/labyrinthe-scratch-768x766.png 768w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2020\/10\/labyrinthe-scratch.png 914w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-5c3e396 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5c3e396\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-ef8a242\" data-id=\"ef8a242\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c1effb3 elementor-widget elementor-widget-spacer\" data-id=\"c1effb3\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-84a06d0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"84a06d0\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-eb23175\" data-id=\"eb23175\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-d919872 elementor-widget elementor-widget-heading\" data-id=\"d919872\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Chapitre 19 : Angles dans un triangle<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-36da94e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"36da94e\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-d5f37c7\" data-id=\"d5f37c7\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ad66d48 elementor-widget elementor-widget-spacer\" data-id=\"ad66d48\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-69a546a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"69a546a\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-0dea2b9\" data-id=\"0dea2b9\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b404aa2 elementor-widget elementor-widget-heading\" data-id=\"b404aa2\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">A) Somme des mesures des angles dans un triangle<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-df97bda elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"df97bda\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-50519a7\" data-id=\"50519a7\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e99c19f elementor-widget elementor-widget-text-editor\" data-id=\"e99c19f\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Propri\u00e9t\u00e9 :<\/strong> Dans un triangle, la somme des mesures des trois angles est \u00e9gale \u00e0 $180\\text{\u00b0}$.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-9d192bc elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9d192bc\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-e4dab3a\" data-id=\"e4dab3a\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a21bc6f elementor-widget elementor-widget-text-editor\" data-id=\"a21bc6f\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>D\u00e9monstration :<\/strong><br \/>On trace la parall\u00e8le \u00e0 la droite $(BC)$ passant par $A$.<br \/>Les angles rouges sont alternes-internes ainsi que les angles verts. Or, d\u2019apr\u00e8s la propri\u00e9t\u00e9 pr\u00e9c\u00e9dente, si deux droites parall\u00e8les sont coup\u00e9es par une s\u00e9cante, alors les angles alternes-internes qu\u2019elles forment ont la m\u00eame mesure.<br \/>Ainsi, les angles rouges ont la m\u00eame mesure et les angles verts ont la m\u00eame mesure.<br \/>On en d\u00e9duit que dans le triangle $ABC$ :<br \/>\\[\\widehat{ABC}+\\widehat{ACB}+\\widehat{BAC}=180\\text{\u00b0}\\]\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-790c713\" data-id=\"790c713\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1ec074a elementor-widget elementor-widget-image\" data-id=\"1ec074a\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"481\" height=\"216\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2022\/05\/angle-triangle-1.png\" class=\"attachment-large size-large wp-image-14087\" alt=\"D\u00e9monstration de la propri\u00e9t\u00e9 de la somme des mesures des angles d&#039;un triangle\" srcset=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2022\/05\/angle-triangle-1.png 481w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2022\/05\/angle-triangle-1-300x135.png 300w\" sizes=\"auto, (max-width: 481px) 100vw, 481px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-01c0538 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"01c0538\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-0ec1c3b\" data-id=\"0ec1c3b\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e9b0fea elementor-widget elementor-widget-video\" data-id=\"e9b0fea\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/VaNDDTPf6cM&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-f9a98f6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f9a98f6\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-b586b40\" data-id=\"b586b40\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c44cdff elementor-widget elementor-widget-text-editor\" data-id=\"c44cdff\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Exemple :<\/strong> Calculer la mesure de l&rsquo;angle $\\widehat{DEF}$.<\/p><p>Dans un triangle, la somme des mesures des angles \u00e9gales $180\\text{\u00b0}$. Ainsi :<br \/>$\\widehat{DEF}+\\widehat{DFE}+\\widehat{FDE}=180\\text{\u00b0}$<br \/>$\\widehat{DEF}+36\\text{\u00b0}+20\\text{\u00b0}=180\\text{\u00b0}$<br \/>$\\widehat{DEF}=180\\text{\u00b0}-(20\\text{\u00b0}+36\\text{\u00b0})$<br \/>$\\widehat{DEF}=180\\text{\u00b0}-56\\text{\u00b0}$<br \/>$\\widehat{DEF}=124\\text{\u00b0}$<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-866b839\" data-id=\"866b839\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3be8bf5 elementor-widget elementor-widget-image\" data-id=\"3be8bf5\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"509\" height=\"243\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2022\/05\/angle-triangle-2.png\" class=\"attachment-large size-large wp-image-14088\" alt=\"Calculer la mesure d&#039;un angle d&#039;un triangle\" srcset=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2022\/05\/angle-triangle-2.png 509w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2022\/05\/angle-triangle-2-300x143.png 300w\" sizes=\"auto, (max-width: 509px) 100vw, 509px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-fe06034 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"fe06034\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-2493bc0\" data-id=\"2493bc0\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f9a9940 elementor-widget elementor-widget-text-editor\" data-id=\"f9a9940\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Exemple :<\/strong> Le triangle $IJK$ est rectangle isoc\u00e8le en $I$. Calculer la mesure de l&rsquo;angle $\\widehat{IKJ}$.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-da6a381 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"da6a381\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-6b1d109\" data-id=\"6b1d109\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-27b0a5c elementor-widget elementor-widget-text-editor\" data-id=\"27b0a5c\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>$IKJ$ est isoc\u00e8le en $I$ donc ses angles \u00e0 la base ont la m\u00eame mesure.<br \/>Ainsi, $\\widehat{IKJ}=\\widehat{IJK}$.<br \/>Ainsi :<br \/>$\\widehat{IKJ}=\\dfrac{180\\text{\u00b0}-90\\text{\u00b0}}{2}=45\\text{\u00b0}$<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-bb0d7e1\" data-id=\"bb0d7e1\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-17a4831 elementor-widget elementor-widget-image\" data-id=\"17a4831\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"367\" height=\"210\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2022\/05\/angle-triangle-3.png\" class=\"attachment-large size-large wp-image-14089\" alt=\"Calculer la mesure d&#039;un angle dans un triangle rectangle isoc\u00e8le\" srcset=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2022\/05\/angle-triangle-3.png 367w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2022\/05\/angle-triangle-3-300x172.png 300w\" sizes=\"auto, (max-width: 367px) 100vw, 367px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7375ce5 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7375ce5\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-154366d\" data-id=\"154366d\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0385f28 elementor-widget elementor-widget-video\" data-id=\"0385f28\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/7CZrbIkWUc4?si=Nm65A4lkjWH-z2YI&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-de85509 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"de85509\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-c005bc7\" data-id=\"c005bc7\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2696ef0 elementor-widget elementor-widget-spacer\" data-id=\"2696ef0\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-f00a40d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f00a40d\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-5f1bed1\" data-id=\"5f1bed1\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e166138 elementor-widget elementor-widget-heading\" data-id=\"e166138\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">B) Triangle \u00e9quilat\u00e9ral<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-5b759a7 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5b759a7\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-b3a6ec1\" data-id=\"b3a6ec1\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f95b171 elementor-widget elementor-widget-text-editor\" data-id=\"f95b171\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Propri\u00e9t\u00e9 :<\/strong> Si un triangle est \u00e9quilat\u00e9ral alors chacun de ses angles mesure $60\\text{\u00b0}$.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7789117 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7789117\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-6231e1d\" data-id=\"6231e1d\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-14f180f elementor-widget elementor-widget-text-editor\" data-id=\"14f180f\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Exemple :<\/strong><\/p>\n<p>Le triangle $IJK$ est \u00e9quilat\u00e9ral donc ses 3 angles ont la m\u00eame mesure.<br>$\\widehat{IJK}=\\widehat{IKJ}=\\widehat{JIK}$.<br>Donc $3\\times \\widehat{IJK}=180\\text{\u00b0}$.<br>Ainsi $\\widehat{IJK}=\\widehat{IKJ}=\\widehat{JIK}=60\\text{\u00b0}$.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-12b8660\" data-id=\"12b8660\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-94c3783 elementor-widget elementor-widget-image\" data-id=\"94c3783\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"243\" height=\"216\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2022\/05\/angle-triangle-4.png\" class=\"attachment-large size-large wp-image-14090\" alt=\"Calcul de mesure d&#039;un angle dans un triangle \u00e9quilat\u00e9ral\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-8b68473 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8b68473\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-daa0fa2\" data-id=\"daa0fa2\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-cf93177 elementor-widget elementor-widget-spacer\" data-id=\"cf93177\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-0f0f362 elementor-section-boxed elementor-section-height-default elementor-section-height-default elementor-invisible\" data-id=\"0f0f362\" data-element_type=\"section\" data-settings=\"{&quot;animation&quot;:&quot;zoomIn&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-a4a2672\" data-id=\"a4a2672\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b753983 elementor-button-info elementor-align-center elementor-widget elementor-widget-button\" data-id=\"b753983\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-xl\" href=\"https:\/\/nuage02.apps.education.fr\/index.php\/s\/ZGfaL9C24fBDAYZ\" target=\"_blank\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-icon elementor-align-icon-left\">\n\t\t\t\t<i aria-hidden=\"true\" class=\"far fa-arrow-alt-circle-right\"><\/i>\t\t\t<\/span>\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Exercices corrig\u00e9s<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-9686c3b elementor-section-boxed elementor-section-height-default elementor-section-height-default elementor-invisible\" data-id=\"9686c3b\" data-element_type=\"section\" data-settings=\"{&quot;animation&quot;:&quot;zoomIn&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-bf7c44c\" data-id=\"bf7c44c\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-19c6ec6 elementor-button-info elementor-align-center elementor-widget elementor-widget-button\" data-id=\"19c6ec6\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-xl\" href=\"https:\/\/creteil.college-willy-ronis.fr\/course\/view.php?id=3\" target=\"_blank\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-icon elementor-align-icon-left\">\n\t\t\t\t<i aria-hidden=\"true\" class=\"far fa-arrow-alt-circle-right\"><\/i>\t\t\t<\/span>\n\t\t\t\t\t\t<span class=\"elementor-button-text\">J'acc\u00e8de \u00e0 d'autres ressources<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Chapitre 19 Angles dans un triangle Chapitre 19 : Angles dans un triangle A) Somme des mesures des angles dans un triangle Propri\u00e9t\u00e9 : Dans un triangle, la somme des mesures des trois angles est \u00e9gale \u00e0 $180text{\u00b0}$. D\u00e9monstration :On trace la parall\u00e8le \u00e0 la droite $(BC)$ passant par $A$.Les angles rouges sont alternes-internes ainsi [&hellip;]<\/p>\n","protected":false},"author":7440,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"site-sidebar-layout":"no-sidebar","site-content-layout":"page-builder","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"disabled","site-post-title":"disabled","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[33],"tags":[],"class_list":["post-13952","post","type-post","status-publish","format-standard","hentry","category-cours-et-exercices-5eme"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v24.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Chapitre 19 : Somme des mesures des angles d&#039;un triangle - 5\u00e8me<\/title>\n<meta name=\"description\" content=\"Cours de math\u00e9matiques de 5\u00e8me sur la somme des mesures des angles d&#039;un triangle, l&#039;activit\u00e9 du chapitre, les exercices corrig\u00e9s...\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/college-willy-ronis.fr\/maths\/chapitre-19-somme-des-mesures-des-angles-dun-triangle\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Chapitre 19 : Somme des mesures des angles d&#039;un triangle - 5\u00e8me\" \/>\n<meta property=\"og:description\" content=\"Cours de math\u00e9matiques de 5\u00e8me sur la somme des mesures des angles d&#039;un triangle, l&#039;activit\u00e9 du chapitre, les exercices corrig\u00e9s...\" \/>\n<meta property=\"og:url\" content=\"https:\/\/college-willy-ronis.fr\/maths\/chapitre-19-somme-des-mesures-des-angles-dun-triangle\/\" \/>\n<meta property=\"og:site_name\" content=\"Math\u00e9matiques au coll\u00e8ge Willy Ronis\" \/>\n<meta property=\"article:published_time\" content=\"2022-05-09T11:47:10+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-04-17T04:37:05+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2020\/10\/labyrinthe-scratch.png\" \/>\n\t<meta property=\"og:image:width\" content=\"914\" \/>\n\t<meta property=\"og:image:height\" content=\"912\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"eric_moisan@orange.fr\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u00c9crit par\" \/>\n\t<meta name=\"twitter:data1\" content=\"eric_moisan@orange.fr\" \/>\n\t<meta name=\"twitter:label2\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/college-willy-ronis.fr\/maths\/chapitre-19-somme-des-mesures-des-angles-dun-triangle\/\",\"url\":\"https:\/\/college-willy-ronis.fr\/maths\/chapitre-19-somme-des-mesures-des-angles-dun-triangle\/\",\"name\":\"Chapitre 19 : Somme des mesures des angles d'un triangle - 5\u00e8me\",\"isPartOf\":{\"@id\":\"https:\/\/college-willy-ronis.fr\/maths\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/college-willy-ronis.fr\/maths\/chapitre-19-somme-des-mesures-des-angles-dun-triangle\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/college-willy-ronis.fr\/maths\/chapitre-19-somme-des-mesures-des-angles-dun-triangle\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2020\/10\/labyrinthe-scratch-300x300.png\",\"datePublished\":\"2022-05-09T11:47:10+00:00\",\"dateModified\":\"2026-04-17T04:37:05+00:00\",\"author\":{\"@id\":\"https:\/\/college-willy-ronis.fr\/maths\/#\/schema\/person\/d202e67a67b7b4f358f706eee0254cbc\"},\"description\":\"Cours de math\u00e9matiques de 5\u00e8me sur la somme des mesures des angles d'un triangle, l'activit\u00e9 du chapitre, les exercices corrig\u00e9s...\",\"breadcrumb\":{\"@id\":\"https:\/\/college-willy-ronis.fr\/maths\/chapitre-19-somme-des-mesures-des-angles-dun-triangle\/#breadcrumb\"},\"inLanguage\":\"fr-FR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/college-willy-ronis.fr\/maths\/chapitre-19-somme-des-mesures-des-angles-dun-triangle\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"fr-FR\",\"@id\":\"https:\/\/college-willy-ronis.fr\/maths\/chapitre-19-somme-des-mesures-des-angles-dun-triangle\/#primaryimage\",\"url\":\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2020\/10\/labyrinthe-scratch.png\",\"contentUrl\":\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2020\/10\/labyrinthe-scratch.png\",\"width\":914,\"height\":912,\"caption\":\"cours de 5\u00e8me\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/college-willy-ronis.fr\/maths\/chapitre-19-somme-des-mesures-des-angles-dun-triangle\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Accueil\",\"item\":\"https:\/\/college-willy-ronis.fr\/maths\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Chapitre 19 : Somme des mesures des angles d&rsquo;un triangle\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/college-willy-ronis.fr\/maths\/#website\",\"url\":\"https:\/\/college-willy-ronis.fr\/maths\/\",\"name\":\"Math\u00e9matiques au coll\u00e8ge Willy Ronis\",\"description\":\"Cours et exercices corrig\u00e9s de math\u00e9matiques de la 6\u00e8me \u00e0 la 3\u00e8me, sujets de brevet, cartes mentales et activit\u00e9s.\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/college-willy-ronis.fr\/maths\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"fr-FR\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/college-willy-ronis.fr\/maths\/#\/schema\/person\/d202e67a67b7b4f358f706eee0254cbc\",\"name\":\"eric_moisan@orange.fr\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"fr-FR\",\"@id\":\"https:\/\/college-willy-ronis.fr\/maths\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/97378c19de3b180e65e886a4976c355a?s=96&d=monsterid&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/97378c19de3b180e65e886a4976c355a?s=96&d=monsterid&r=g\",\"caption\":\"eric_moisan@orange.fr\"},\"url\":\"https:\/\/college-willy-ronis.fr\/maths\/author\/eric_moisanorange-fr\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Chapitre 19 : Somme des mesures des angles d'un triangle - 5\u00e8me","description":"Cours de math\u00e9matiques de 5\u00e8me sur la somme des mesures des angles d'un triangle, l'activit\u00e9 du chapitre, les exercices corrig\u00e9s...","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/college-willy-ronis.fr\/maths\/chapitre-19-somme-des-mesures-des-angles-dun-triangle\/","og_locale":"fr_FR","og_type":"article","og_title":"Chapitre 19 : Somme des mesures des angles d'un triangle - 5\u00e8me","og_description":"Cours de math\u00e9matiques de 5\u00e8me sur la somme des mesures des angles d'un triangle, l'activit\u00e9 du chapitre, les exercices corrig\u00e9s...","og_url":"https:\/\/college-willy-ronis.fr\/maths\/chapitre-19-somme-des-mesures-des-angles-dun-triangle\/","og_site_name":"Math\u00e9matiques au coll\u00e8ge Willy Ronis","article_published_time":"2022-05-09T11:47:10+00:00","article_modified_time":"2026-04-17T04:37:05+00:00","og_image":[{"width":914,"height":912,"url":"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2020\/10\/labyrinthe-scratch.png","type":"image\/png"}],"author":"eric_moisan@orange.fr","twitter_card":"summary_large_image","twitter_misc":{"\u00c9crit par":"eric_moisan@orange.fr","Dur\u00e9e de lecture estim\u00e9e":"3 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/college-willy-ronis.fr\/maths\/chapitre-19-somme-des-mesures-des-angles-dun-triangle\/","url":"https:\/\/college-willy-ronis.fr\/maths\/chapitre-19-somme-des-mesures-des-angles-dun-triangle\/","name":"Chapitre 19 : Somme des mesures des angles d'un triangle - 5\u00e8me","isPartOf":{"@id":"https:\/\/college-willy-ronis.fr\/maths\/#website"},"primaryImageOfPage":{"@id":"https:\/\/college-willy-ronis.fr\/maths\/chapitre-19-somme-des-mesures-des-angles-dun-triangle\/#primaryimage"},"image":{"@id":"https:\/\/college-willy-ronis.fr\/maths\/chapitre-19-somme-des-mesures-des-angles-dun-triangle\/#primaryimage"},"thumbnailUrl":"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2020\/10\/labyrinthe-scratch-300x300.png","datePublished":"2022-05-09T11:47:10+00:00","dateModified":"2026-04-17T04:37:05+00:00","author":{"@id":"https:\/\/college-willy-ronis.fr\/maths\/#\/schema\/person\/d202e67a67b7b4f358f706eee0254cbc"},"description":"Cours de math\u00e9matiques de 5\u00e8me sur la somme des mesures des angles d'un triangle, l'activit\u00e9 du chapitre, les exercices corrig\u00e9s...","breadcrumb":{"@id":"https:\/\/college-willy-ronis.fr\/maths\/chapitre-19-somme-des-mesures-des-angles-dun-triangle\/#breadcrumb"},"inLanguage":"fr-FR","potentialAction":[{"@type":"ReadAction","target":["https:\/\/college-willy-ronis.fr\/maths\/chapitre-19-somme-des-mesures-des-angles-dun-triangle\/"]}]},{"@type":"ImageObject","inLanguage":"fr-FR","@id":"https:\/\/college-willy-ronis.fr\/maths\/chapitre-19-somme-des-mesures-des-angles-dun-triangle\/#primaryimage","url":"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2020\/10\/labyrinthe-scratch.png","contentUrl":"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2020\/10\/labyrinthe-scratch.png","width":914,"height":912,"caption":"cours de 5\u00e8me"},{"@type":"BreadcrumbList","@id":"https:\/\/college-willy-ronis.fr\/maths\/chapitre-19-somme-des-mesures-des-angles-dun-triangle\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Accueil","item":"https:\/\/college-willy-ronis.fr\/maths\/"},{"@type":"ListItem","position":2,"name":"Chapitre 19 : Somme des mesures des angles d&rsquo;un triangle"}]},{"@type":"WebSite","@id":"https:\/\/college-willy-ronis.fr\/maths\/#website","url":"https:\/\/college-willy-ronis.fr\/maths\/","name":"Math\u00e9matiques au coll\u00e8ge Willy Ronis","description":"Cours et exercices corrig\u00e9s de math\u00e9matiques de la 6\u00e8me \u00e0 la 3\u00e8me, sujets de brevet, cartes mentales et activit\u00e9s.","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/college-willy-ronis.fr\/maths\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"fr-FR"},{"@type":"Person","@id":"https:\/\/college-willy-ronis.fr\/maths\/#\/schema\/person\/d202e67a67b7b4f358f706eee0254cbc","name":"eric_moisan@orange.fr","image":{"@type":"ImageObject","inLanguage":"fr-FR","@id":"https:\/\/college-willy-ronis.fr\/maths\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/97378c19de3b180e65e886a4976c355a?s=96&d=monsterid&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/97378c19de3b180e65e886a4976c355a?s=96&d=monsterid&r=g","caption":"eric_moisan@orange.fr"},"url":"https:\/\/college-willy-ronis.fr\/maths\/author\/eric_moisanorange-fr\/"}]}},"_links":{"self":[{"href":"https:\/\/college-willy-ronis.fr\/maths\/wp-json\/wp\/v2\/posts\/13952","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/college-willy-ronis.fr\/maths\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/college-willy-ronis.fr\/maths\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/college-willy-ronis.fr\/maths\/wp-json\/wp\/v2\/users\/7440"}],"replies":[{"embeddable":true,"href":"https:\/\/college-willy-ronis.fr\/maths\/wp-json\/wp\/v2\/comments?post=13952"}],"version-history":[{"count":12,"href":"https:\/\/college-willy-ronis.fr\/maths\/wp-json\/wp\/v2\/posts\/13952\/revisions"}],"predecessor-version":[{"id":19942,"href":"https:\/\/college-willy-ronis.fr\/maths\/wp-json\/wp\/v2\/posts\/13952\/revisions\/19942"}],"wp:attachment":[{"href":"https:\/\/college-willy-ronis.fr\/maths\/wp-json\/wp\/v2\/media?parent=13952"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/college-willy-ronis.fr\/maths\/wp-json\/wp\/v2\/categories?post=13952"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/college-willy-ronis.fr\/maths\/wp-json\/wp\/v2\/tags?post=13952"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}