{"id":245352,"date":"2025-07-06T04:58:04","date_gmt":"2025-07-06T04:58:04","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=245352"},"modified":"2025-07-06T04:58:06","modified_gmt":"2025-07-06T04:58:06","slug":"find-the-values-of-x-and-y","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/06\/find-the-values-of-x-and-y\/","title":{"rendered":"Find the values of x and y\u00a0"},"content":{"rendered":"\n<pre id=\"preorder-ask-header-text\" class=\"wp-block-preformatted\">Find the values of x and y&nbsp;<\/pre>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/image-218.png\" alt=\"\" class=\"wp-image-245353\"\/><\/figure>\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>Based on the provided image, here are the values for x and y.<\/p>\n\n\n\n<p><strong>Correct Answer:<\/strong><br>x = 4<br>y = 4<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>The problem states that triangle ABC is congruent to triangle DEF, written as \u0394ABC \u2245 \u0394DEF. This congruence means that all corresponding parts of the two triangles\u2014their sides and angles\u2014are equal. The order of the vertices in the congruence statement tells us which parts correspond.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Corresponding Sides:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Side AB corresponds to side DE.<\/li>\n\n\n\n<li>Side BC corresponds to side EF.<\/li>\n\n\n\n<li>Side AC corresponds to side DF.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Corresponding Angles:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Angle A corresponds to Angle D (\u2220A \u2245 \u2220D).<\/li>\n\n\n\n<li>Angle B corresponds to Angle E (\u2220B \u2245 \u2220E).<\/li>\n\n\n\n<li>Angle C corresponds to Angle F (\u2220C \u2245 \u2220F).<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<p><strong>Step 1: Find the value of x.<\/strong><br>From the diagram, we are given the lengths of the corresponding sides AB and DE.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Length of AB = 10 in.<\/li>\n\n\n\n<li>Length of DE = (4x &#8211; 6) in.<\/li>\n<\/ul>\n\n\n\n<p>Since AB and DE are corresponding sides of congruent triangles, their lengths must be equal. We can set up an equation:<br>AB = DE<br>10 = 4x &#8211; 6<\/p>\n\n\n\n<p>To solve for x, first add 6 to both sides of the equation:<br>10 + 6 = 4x<br>16 = 4x<\/p>\n\n\n\n<p>Now, divide both sides by 4:<br>x = 16 \/ 4<br><strong>x = 4<\/strong><\/p>\n\n\n\n<p><strong>Step 2: Find the value of y.<\/strong><br>From the diagram, we are given the measures of the corresponding angles C and F.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Measure of Angle C = (14x + y)\u00b0<\/li>\n\n\n\n<li>Measure of Angle F = 60\u00b0<\/li>\n<\/ul>\n\n\n\n<p>Since \u2220C and \u2220F are corresponding angles, their measures are equal. We can set up another equation:<br>m\u2220C = m\u2220F<br>14x + y = 60<\/p>\n\n\n\n<p>We already found that x = 4. We can substitute this value into the equation to solve for y:<br>14(4) + y = 60<br>56 + y = 60<\/p>\n\n\n\n<p>To find y, subtract 56 from both sides of the equation:<br>y = 60 &#8211; 56<br><strong>y = 4<\/strong><\/p>\n\n\n\n<p>Thus, the values are x = 4 and y = 4.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-635.jpeg\" alt=\"\" class=\"wp-image-245354\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Find the values of x and y&nbsp; The Correct Answer and Explanation is: Based on the provided image, here are the values for x and y. Correct Answer:x = 4y = 4 Explanation: The problem states that triangle ABC is congruent to triangle DEF, written as \u0394ABC \u2245 \u0394DEF. This congruence means that all corresponding [&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-245352","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245352","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=245352"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245352\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=245352"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=245352"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=245352"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}