{"id":13383,"date":"2018-01-29T19:10:00","date_gmt":"2018-01-29T19:10:00","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13383"},"modified":"2022-01-17T11:19:23","modified_gmt":"2022-01-17T11:19:23","slug":"um-decagono-regular","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13383","title":{"rendered":"Um dec\u00e1gono regular"},"content":{"rendered":"<p><ul id='GTTabs_ul_13383' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13383' class='GTTabs_curr'><a  id=\"13383_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13383' ><a  id=\"13383_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_13383'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Calcula as amplitudes de cada \u00e2ngulo externo e de cada \u00e2ngulo interno de um dec\u00e1gono regular.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13383' onClick='GTTabs_show(1,13383)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13383'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>A soma das amplitudes, em graus, dos \u00e2ngulos internos de um pol\u00edgono convexo com \\(n\\) lados \u00e9 igual a\u00a0\\({S_i} = \\left( {n &#8211; 2} \\right) \\times 180^\\circ \\).<\/p>\n<p>Num pol\u00edgono convexo, qualquer que seja o n\u00famero de lados, a soma das medidas das amplitudes de\u00a0\\(n\\) \u00e2ngulos externos com v\u00e9rtices distintos \u00e9 igual a um \u00e2ngulo giro, isto \u00e9,\u00a0\\({S_e} = 360^\\circ \\).<\/p>\n<\/blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/Regular_polygon_10_annotated.svg.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13386\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13386\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/Regular_polygon_10_annotated.svg.png\" data-orig-size=\"469,480\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Dec\u00e1gono regular\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/Regular_polygon_10_annotated.svg.png\" class=\"alignright size-medium wp-image-13386\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/Regular_polygon_10_annotated.svg-293x300.png\" alt=\"\" width=\"293\" height=\"300\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/Regular_polygon_10_annotated.svg-293x300.png 293w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/Regular_polygon_10_annotated.svg.png 469w\" sizes=\"auto, (max-width: 293px) 100vw, 293px\" \/><\/a>Comecemos por determinar a soma das amplitudes dos \u00e2ngulos internos do dec\u00e1gono regular:\u00a0\\({S_i} = \\left( {10 &#8211; 2} \\right) \\times 180^\\circ = 1440^\\circ \\).<\/p>\n<p>Como o pol\u00edgono \u00e9 regular, ent\u00e3o os \u00e2ngulos internos s\u00e3o geometricamente iguais, sendo \\(\\alpha = \\frac{{1440^\\circ }}{{10}} = 144^\\circ \\) a amplitude de cada um deles.<\/p>\n<p>A soma das amplitudes dos seus dez \u00e2ngulos externos, considerando um em cada v\u00e9rtice, \u00e9\u00a0\\({S_e} = 360^\\circ \\).<br \/>\nComo os \u00e2ngulos externos s\u00e3o tamb\u00e9m geometricamente iguais entre si, a amplitude de cada um deles \u00e9 \\(\\beta = \\frac{{360^\\circ }}{{10}} = 36^\\circ \\).<\/p>\n<\/p>\n<p><strong>Nota<\/strong>: Em alternativa, tamb\u00e9m poder\u00e1 ser tido em considera\u00e7\u00e3o que, em cada v\u00e9rtice, o \u00e2ngulo interno e o externo s\u00e3o adjacentes suplementares a par com uma das rela\u00e7\u00f5es anteriores (\\({S_i}\\) ou \\({S_e}\\)).<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13383' onClick='GTTabs_show(0,13383)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Calcula as amplitudes de cada \u00e2ngulo externo e de cada \u00e2ngulo interno de um dec\u00e1gono regular. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20482,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,278],"tags":[426,465,464,188],"series":[],"class_list":["post-13383","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-circunferencia-e-poligonos","tag-9-o-ano","tag-angulo-externo","tag-angulo-interno","tag-circunferencia"],"views":5157,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag143-4_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13383","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=13383"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13383\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20482"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13383"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13383"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13383"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13383"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}