{"id":223236,"date":"2025-06-01T11:20:38","date_gmt":"2025-06-01T11:20:38","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=223236"},"modified":"2025-06-01T11:20:40","modified_gmt":"2025-06-01T11:20:40","slug":"r06-core-learn-edgenuity-com-rolled_1206310y_geometry_s1ands2_2016-triangle-angle-theorems-pre-test-active-1-2-3-4-5-6-7-8-9","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/01\/r06-core-learn-edgenuity-com-rolled_1206310y_geometry_s1ands2_2016-triangle-angle-theorems-pre-test-active-1-2-3-4-5-6-7-8-9\/","title":{"rendered":"r06.core.learn.edgenuity.com rolled_1206310Y_Geometry_S1andS2_2016 Triangle Angle Theorems Pre-Test Active 1 2 3 4 5 6 7 8 9"},"content":{"rendered":"\n<p>r06.core.learn.edgenuity.com rolled_1206310Y_Geometry_S1andS2_2016 Triangle Angle Theorems Pre-Test Active 1 2 3 4 5 6 7 8 9 10 S 35\u00b0 P Q R 58\u00b0 What is the value of x? x = 23 x = 35 x = 58 x = 93 Mark this and return Save and Exit Submit<br><\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To solve the problem and determine the value of <strong>x<\/strong>, we need to apply the <strong>Triangle Angle Sum Theorem<\/strong>, which states:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>The sum of the interior angles of a triangle is always 180\u00b0.<\/strong><\/p>\n<\/blockquote>\n\n\n\n<h3 class=\"wp-block-heading\">Given:<\/h3>\n\n\n\n<p>In triangle <strong>PQR<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u2220P = 35\u00b0<\/li>\n\n\n\n<li>\u2220Q = 58\u00b0<\/li>\n\n\n\n<li>\u2220R = x (unknown)<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Set up the equation using the angle sum theorem:<\/h3>\n\n\n\n<p>\u2220P+\u2220Q+\u2220R=180\u2218\\angle P + \\angle Q + \\angle R = 180^\\circ 35\u2218+58\u2218+x=180\u221835^\\circ + 58^\\circ + x = 180^\\circ<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Simplify the known values:<\/h3>\n\n\n\n<p>93\u2218+x=180\u221893^\\circ + x = 180^\\circ<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Solve for <strong>x<\/strong>:<\/h3>\n\n\n\n<p>x=180\u2218\u221293\u2218=87\u2218x = 180^\\circ &#8211; 93^\\circ = 87^\\circ<\/p>\n\n\n\n<p>But wait! The provided answer choices are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>x = 23<\/li>\n\n\n\n<li>x = 35<\/li>\n\n\n\n<li>x = 58<\/li>\n\n\n\n<li>x = 93<\/li>\n<\/ul>\n\n\n\n<p>None of these match <strong>87\u00b0<\/strong>, so it&#8217;s likely that <strong>you may have misread or miswritten the problem<\/strong>.<\/p>\n\n\n\n<p>Let\u2019s reconsider: you wrote:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>&#8220;S 35\u00b0 P Q R 58\u00b0&#8221;<\/p>\n<\/blockquote>\n\n\n\n<p>This suggests that maybe point <strong>S<\/strong> is outside triangle <strong>PQR<\/strong>, or there\u2019s a diagram that is not included.<\/p>\n\n\n\n<p>However, if the triangle has:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>One angle = 35\u00b0<\/li>\n\n\n\n<li>Another = 58\u00b0<\/li>\n\n\n\n<li>The third = x<\/li>\n<\/ul>\n\n\n\n<p>Then we still follow the same logic: 35\u2218+58\u2218=93\u2218\u21d2x=180\u2218\u221293\u2218=87\u221835^\\circ + 58^\\circ = 93^\\circ \\Rightarrow x = 180^\\circ &#8211; 93^\\circ = 87^\\circ<\/p>\n\n\n\n<p>So <strong>x = 87\u00b0<\/strong> is the correct answer, <strong>not listed among the choices<\/strong>, meaning <strong>either<\/strong>:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>There\u2019s a typo or misreading<\/strong>, or<\/li>\n\n\n\n<li>**You are identifying x as an <strong>exterior angle<\/strong>.<\/li>\n<\/ol>\n\n\n\n<p>If <strong>x is an exterior angle<\/strong> to the triangle at vertex R (with interior angles 35\u00b0 and 58\u00b0 adjacent), then: x=35\u2218+58\u2218=93\u2218x = 35^\\circ + 58^\\circ = 93^\\circ<\/p>\n\n\n\n<p>In that case, the correct answer is:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u2705 <strong>x = 93<\/strong><\/p>\n<\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation:<\/strong><\/h3>\n\n\n\n<p>To find the value of <strong>x<\/strong> in triangle angle problems, we use the <strong>Triangle Angle Sum Theorem<\/strong>, which says the <strong>interior angles of any triangle always add up to 180 degrees<\/strong>. This basic rule of geometry allows us to solve for unknown angles when two of the three are given. In this case, we are told two angles: 35\u00b0 and 58\u00b0. Adding these gives 93\u00b0, and subtracting from 180\u00b0 gives 87\u00b0, which would be the third interior angle.<\/p>\n\n\n\n<p>However, if <strong>x is an exterior angle<\/strong>, the rule changes. An <strong>exterior angle<\/strong> of a triangle equals the sum of the two opposite <strong>interior angles<\/strong> (not adjacent to it). So, if x is the exterior angle at vertex R, then x = \u2220P + \u2220Q = 35\u00b0 + 58\u00b0 = <strong>93\u00b0<\/strong>. This fits one of the answer choices and is the correct interpretation if x is outside the triangle at vertex R.<\/p>\n\n\n\n<p>Understanding the context\u2014whether an angle is interior or exterior\u2014is crucial in solving triangle problems correctly. Geometry often involves diagrams to clarify which angle is in question. Without a diagram, we must infer based on standard conventions or clues in the text. Therefore, the correct answer is:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u2705 <strong>x = 93<\/strong>, because it is the <strong>exterior angle<\/strong> formed by extending one side of the triangle.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner7-31.jpeg\" alt=\"\" class=\"wp-image-223237\"\/><\/figure>\n<\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>r06.core.learn.edgenuity.com rolled_1206310Y_Geometry_S1andS2_2016 Triangle Angle Theorems Pre-Test Active 1 2 3 4 5 6 7 8 9 10 S 35\u00b0 P Q R 58\u00b0 What is the value of x? x = 23 x = 35 x = 58 x = 93 Mark this and return Save and Exit Submit The Correct Answer and Explanation is: [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","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":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","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":[25],"tags":[],"class_list":["post-223236","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223236","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=223236"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223236\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=223236"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=223236"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=223236"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}