{"id":3408,"date":"2010-10-03T16:34:53","date_gmt":"2010-10-03T15:34:53","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=3408"},"modified":"2022-01-18T22:28:24","modified_gmt":"2022-01-18T22:28:24","slug":"os-angulos","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=3408","title":{"rendered":"Os \u00e2ngulos"},"content":{"rendered":"<p><ul id='GTTabs_ul_3408' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_3408' class='GTTabs_curr'><a  id=\"3408_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_3408' ><a  id=\"3408_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_3408'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/angulos.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"3411\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=3411\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/angulos.jpg\" data-orig-size=\"312,122\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;HP pstc4380&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;}\" data-image-title=\"Os \u00e2ngulos\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/angulos.jpg\" class=\"alignright wp-image-3411 size-full\" title=\"Os \u00e2ngulos\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/angulos.jpg\" alt=\"\" width=\"312\" height=\"122\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/angulos.jpg 312w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/angulos-300x117.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/angulos-150x58.jpg 150w\" sizes=\"auto, (max-width: 312px) 100vw, 312px\" \/><\/a>Observa os \u00e2ngulos.<\/p>\n<p>Qual \u00e9 o valor de $x$?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_3408' onClick='GTTabs_show(1,3408)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_3408'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"3417\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=3417\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/angulos2.jpg\" data-orig-size=\"312,122\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;HP pstc4380&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;}\" data-image-title=\"Os \u00e2ngulos 2\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/angulos2.jpg\" class=\"alignright wp-image-3417 size-full\" title=\"Os \u00e2ngulos 2\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/angulos2.jpg\" alt=\"\" width=\"312\" height=\"122\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/angulos2.jpg 312w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/angulos2-300x117.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/angulos2-150x58.jpg 150w\" sizes=\"auto, (max-width: 312px) 100vw, 312px\" \/>Considerando que a soma dos dois \u00e2ngulos considerados \u00e9 um \u00e2ngulo raso, cuja amplitude \u00e9 180\u00ba, temos: \\[\\begin{array}{*{35}{l}}<br \/>\n(4x-18)+(3x+30)=180 &amp; \\Leftrightarrow\u00a0 &amp; 4x-18+3x+30=180\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; 7x=180-12\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; \\frac{7x}{7}=\\frac{168}{7}\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; x=24\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<p>Assim, para $x=24$, temos:<\/p>\n<ul>\n<li>$A\\widehat{V}B=4\\times 24{}^\\text{o}-18{}^\\text{o}=78{}^\\text{o}$<\/li>\n<li>$B\\widehat{V}C=3\\times 24{}^\\text{o}+30{}^\\text{o}=102{}^\\text{o}$<\/li>\n<li>$A\\widehat{V}B+B\\widehat{V}C=78{}^\\text{o}+102{}^\\text{o}=180{}^\\text{o}$<\/li>\n<\/ul>\n<p>Portanto, $x=24$ (graus).<\/p>\n<p>Tens algum coment\u00e1rio a fazer sobre a figura dada? Porqu\u00ea?<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_3408' onClick='GTTabs_show(0,3408)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Observa os \u00e2ngulos. Qual \u00e9 o valor de $x$? Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20611,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,101],"tags":[424,425],"series":[],"class_list":["post-3408","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-equacoes","tag-8-o-ano","tag-equacoes"],"views":2975,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/7V2Pag066-12_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/3408","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=3408"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/3408\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20611"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3408"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3408"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3408"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=3408"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}