{"id":4585,"date":"2010-10-25T02:27:59","date_gmt":"2010-10-25T01:27:59","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=4585"},"modified":"2022-01-19T00:14:47","modified_gmt":"2022-01-19T00:14:47","slug":"calcula-o-valor-de-x-em-cada-figura","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=4585","title":{"rendered":"Calcula o valor de x em cada figura"},"content":{"rendered":"<p><ul id='GTTabs_ul_4585' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_4585' class='GTTabs_curr'><a  id=\"4585_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_4585' ><a  id=\"4585_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_4585'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><span style=\"text-decoration: underline;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag103-2.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"4588\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=4588\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag103-2.jpg\" data-orig-size=\"555,921\" 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=\"Rectas paralelas\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag103-2.jpg\" class=\"alignright wp-image-4588\" title=\"Rectas paralelas\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag103-2.jpg\" alt=\"\" width=\"300\" height=\"498\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag103-2.jpg 555w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag103-2-180x300.jpg 180w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag103-2-90x150.jpg 90w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag103-2-400x663.jpg 400w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/span>Calcula o valor de x em cada figura, considerando r\/\/s.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_4585' onClick='GTTabs_show(1,4585)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_4585'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag103-2.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"4588\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=4588\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag103-2.jpg\" data-orig-size=\"555,921\" 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=\"Rectas paralelas\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag103-2.jpg\" class=\"alignright wp-image-4588\" title=\"Rectas paralelas\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag103-2.jpg\" alt=\"\" width=\"300\" height=\"498\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag103-2.jpg 555w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag103-2-180x300.jpg 180w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag103-2-90x150.jpg 90w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag103-2-400x663.jpg 400w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>FIGURA a)<\/span><\/strong><\/p>\n<p>Os \u00e2ngulos considerados s\u00e3o geometricamente iguais, pois s\u00e3o ambos agudos\u00a0e de lados paralelos.<br \/>\nLogo, temos:<\/p>\n<p style=\"text-align: center;\">$\\begin{array}{*{35}{l}}<br \/>\n2x-95=25 &amp; \\Leftrightarrow\u00a0 &amp; 2x=120\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; x=60\u00a0 \\\\<br \/>\n\\end{array}$<\/p>\n<p>Portanto, $x=60{}^\\text{o}$.<\/p>\n<p><span style=\"text-decoration: underline;\"><strong>FIGURA b)<\/strong><\/span><\/p>\n<p>Os \u00e2ngulos considerados s\u00e3o suplementares pois, sendo um agudo e outro obtuso, possuem lados paralelos:<br \/>\nLogo, temos:<\/p>\n<p style=\"text-align: center;\">$\\begin{array}{*{35}{l}}<br \/>\n(5x+30)+(x+6)=180 &amp; \\Leftrightarrow\u00a0 &amp; 5x+x=180-30-6\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; 6x=144\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; x=24\u00a0 \\\\<br \/>\n\\end{array}$<\/p>\n<p>Portanto, $x=24{}^\\text{o}$.<\/p>\n<p><span style=\"text-decoration: underline;\"><strong>FIGURA c)<\/strong><\/span><\/p>\n<p>O \u00e2ngulo assinalado a verde \u00e9 um \u00e2ngulo externo do tri\u00e2ngulo. O \u00e2ngulo assinalado a rosa \u00e9 geometricamente igual ao \u00e2ngulo interno n\u00e3o adjacente ao externo considerado, pois ambos s\u00e3o agudos de lados paralelos.<br \/>\nComo a amplitude de um \u00e2ngulo externo de um tri\u00e2ngulo \u00e9 igual \u00e0 soma das amplitudes dos internos n\u00e3o adjacentes, temos:<\/p>\n<p style=\"text-align: center;\">$\\begin{array}{*{35}{l}}<br \/>\n2x+20 &amp; \\Leftrightarrow\u00a0 &amp; x+70\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; 2x-x=70-20\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; x=50\u00a0 \\\\<br \/>\n\\end{array}$<\/p>\n<p>Portanto, $x=50{}^\\text{o}$.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_4585' onClick='GTTabs_show(0,4585)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Calcula o valor de x em cada figura, considerando r\/\/s. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20628,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,102],"tags":[424,105,425],"series":[],"class_list":["post-4585","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-do-espaco-ao-plano","tag-8-o-ano","tag-angulos","tag-equacoes"],"views":13276,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/7V2Pag103-2_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/4585","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=4585"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/4585\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20628"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4585"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4585"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4585"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=4585"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}