{"id":228906,"date":"2025-06-07T18:10:00","date_gmt":"2025-06-07T18:10:00","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=228906"},"modified":"2025-06-07T18:10:02","modified_gmt":"2025-06-07T18:10:02","slug":"2-intersecting-lines-are-shown","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/07\/2-intersecting-lines-are-shown\/","title":{"rendered":"2 intersecting lines are shown."},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">2 intersecting lines are shown. A line with points T, R, W intersects a line with points S, R, V at point R. Angle T R V is 95 degrees. mAngleSRW =<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><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 class=\"wp-block-paragraph\">To find the measure of \u2220SRW given the information:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Two lines intersect at point <strong>R<\/strong>.<\/li>\n\n\n\n<li>One line has points <strong>T, R, W<\/strong>.<\/li>\n\n\n\n<li>The other line has points <strong>S, R, V<\/strong>.<\/li>\n\n\n\n<li>\u2220TRV is 95\u00b0.<\/li>\n\n\n\n<li>We are asked to find <strong>m\u2220SRW<\/strong>.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step-by-Step Solution<\/strong><\/h3>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Step 1: Understand the intersection<\/strong><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">You have two straight lines:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Line 1: T \u2014 R \u2014 W<\/li>\n\n\n\n<li>Line 2: S \u2014 R \u2014 V<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">They intersect at <strong>R<\/strong>. So <strong>R<\/strong> is the common point, and these lines cross each other.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Since <strong>T, R, W<\/strong> lie on one straight line, \u2220TRW is a straight angle = 180\u00b0.<br>Similarly, <strong>S, R, V<\/strong> lie on a straight line, so \u2220SRV = 180\u00b0.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Step 2: Use angle relationships<\/strong><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">We are given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u2220TRV = 95\u00b0. This is the angle between ray <strong>RT<\/strong> and ray <strong>RV<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">We are asked to find:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u2220SRW = the angle between <strong>RS<\/strong> and <strong>RW<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Let\u2019s look at the diagram logically:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u2220TRV and \u2220SRW are <strong>vertical angles<\/strong>. That is, they are opposite each other when two lines intersect.<\/li>\n\n\n\n<li>Vertical angles are always <strong>congruent<\/strong>\u2014they have the same measure.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">So,<br><strong>m\u2220SRW = m\u2220TRV = 95\u00b0<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 <strong>Final Answer:<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>m\u2220SRW = 95\u00b0<\/strong><\/p>\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 class=\"wp-block-paragraph\">When two straight lines intersect, they form <strong>four angles<\/strong> at the point of intersection. Each pair of opposite angles is called <strong>vertical angles<\/strong>. A key property of vertical angles is that they are always <strong>equal in measure<\/strong> because they are formed by the same two intersecting lines, just in opposite directions.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In this problem, we are told that two lines intersect at point R. One line runs through points <strong>T, R, W<\/strong> (forming a straight line), and the other through <strong>S, R, V<\/strong> (also a straight line). The angle \u2220TRV is given as 95\u00b0, which is the angle formed between the directions from R to T and from R to V.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Since these lines intersect, the angle directly opposite \u2220TRV\u2014namely \u2220SRW\u2014is its <strong>vertical angle<\/strong>. The angle \u2220SRW is formed between the directions from R to S and R to W.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">By the <strong>Vertical Angles Theorem<\/strong>, vertical angles are always congruent, meaning they have the same measure. So:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\u2220TRV = \u2220SRW = 95\u00b0<\/p>\n<\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">This property is fundamental in geometry and helps in many problems involving intersecting lines.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Understanding this concept helps students analyze geometric figures without needing to rely on measurements. Instead, we use relationships and properties like vertical angles, linear pairs, and supplementary angles to determine unknown angle measures logically.<\/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-banner4-650.jpeg\" alt=\"\" class=\"wp-image-228907\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>2 intersecting lines are shown. A line with points T, R, W intersects a line with points S, R, V at point R. Angle T R V is 95 degrees. mAngleSRW = The Correct Answer and Explanation is: To find the measure of \u2220SRW given the information: Step-by-Step Solution Step 1: Understand the intersection You [&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-228906","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/228906","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=228906"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/228906\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=228906"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=228906"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=228906"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}