{"id":13375,"date":"2018-01-29T17:29:13","date_gmt":"2018-01-29T17:29:13","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13375"},"modified":"2022-01-17T11:07:02","modified_gmt":"2022-01-17T11:07:02","slug":"um-poligono-regular-de-15-lados","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13375","title":{"rendered":"Um pol\u00edgono regular de 15 lados"},"content":{"rendered":"<p><ul id='GTTabs_ul_13375' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13375' class='GTTabs_curr'><a  id=\"13375_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13375' ><a  id=\"13375_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_13375'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag143-2.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13377\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13377\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag143-2.png\" data-orig-size=\"260,255\" 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=\"9V1Pag143-2\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag143-2.png\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag143-2.png\" class=\"alignright size-full wp-image-13377\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag143-2.png\" alt=\"\" width=\"260\" height=\"255\" \/><\/a>Considera um pol\u00edgono regular de 15 lados.<\/p>\n<ol>\n<li>Qual \u00e9 a amplitude de cada \u00e2ngulo externo?<\/li>\n<li>Qual \u00e9 a soma das amplitudes dos \u00e2ngulos internos?<\/li>\n<li>Qual \u00e9 a amplitude de cada \u00e2ngulo interno?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13375' onClick='GTTabs_show(1,13375)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13375'>\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:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/d\/d0\/Regular_polygon_15_annotated.svg\/482px-Regular_polygon_15_annotated.svg.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignright\" src=\"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/d\/d0\/Regular_polygon_15_annotated.svg\/482px-Regular_polygon_15_annotated.svg.png\" alt=\"\" width=\"310\" height=\"308\" \/><\/a><\/p>\n<ol>\n<li>Como o pol\u00edgono \u00e9 regular, ent\u00e3o os \u00e2ngulos internos s\u00e3o geometricamente iguais, bem como os \u00e2ngulos externos s\u00e3o tamb\u00e9m geometricamente iguais. Assim, a amplitude de cada \u00e2ngulo externo \u00e9 \\(\\beta = \\frac{{360^\\circ }}{{15}} = 24^\\circ \\).<br \/>\n\u00ad<\/li>\n<li>A soma das amplitudes dos \u00e2ngulos internos \u00e9 \\({S_i} = \\left( {15 &#8211; 2} \\right) \\times 180^\\circ = 2340^\\circ \\).<br \/>\n\u00ad<\/li>\n<li>Como os \u00e2ngulos internos s\u00e3o geometricamente iguais, ent\u00e3o a amplitude de cada um \u00e9\u00a0\\(\\alpha = \\frac{{\\left( {15 &#8211; 2} \\right) \\times 180^\\circ }}{{15}} = \\frac{{2340^\\circ }}{{15}} = 156^\\circ \\).<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13375' onClick='GTTabs_show(0,13375)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considera um pol\u00edgono regular de 15 lados. Qual \u00e9 a amplitude de cada \u00e2ngulo externo? Qual \u00e9 a soma das amplitudes dos \u00e2ngulos internos? Qual \u00e9 a amplitude de cada \u00e2ngulo&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20478,"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-13375","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":12524,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag143-2_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13375","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=13375"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13375\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20478"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13375"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13375"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13375"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13375"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}