To solve this problem, we are given:<\/p>\n\n\n\n
- \n
- DEFG is an isosceles trapezoid<\/strong><\/li>\n\n\n\n
- One angle is 118\u00b0<\/strong><\/li>\n\n\n\n
- One angle is 62\u00b0<\/strong><\/li>\n\n\n\n
- We are to find the measure of \u2220D<\/li>\n<\/ul>\n\n\n\n
Step-by-Step Solution<\/h3>\n\n\n\n
Step 1: Understanding an isosceles trapezoid<\/h4>\n\n\n\n
An isosceles trapezoid<\/strong> is a trapezoid in which the non-parallel sides (legs) are congruent. The base angles (angles that share a base) are congruent.<\/p>\n\n\n\n
So:<\/p>\n\n\n\n
- \n
- If \u2220D<\/strong> and \u2220E<\/strong> are on one base (say base DE<\/strong>), then \u2220D \u2245 \u2220E.<\/li>\n\n\n\n
- If \u2220F<\/strong> and \u2220G<\/strong> are on the other base (say base FG<\/strong>), then \u2220F \u2245 \u2220G.<\/li>\n<\/ul>\n\n\n\n
Also, adjacent angles between the base and leg<\/strong> of a trapezoid are supplementary<\/strong> (add up to 180\u00b0).<\/p>\n\n\n\n
Step 2: Using the given information<\/h4>\n\n\n\n
Let\u2019s suppose the following configuration:<\/p>\n\n\n\n
- \n
- \u2220F = 62\u00b0<\/li>\n\n\n\n
- \u2220G = 62\u00b0 (because base angles in isosceles trapezoid are equal)<\/li>\n\n\n\n
- \u2220D and \u2220E must then each be 118\u00b0, since they are adjacent to the 62\u00b0 angles and must add up to 180\u00b0.<\/li>\n<\/ul>\n\n\n\n
Why?
Because in trapezoids, consecutive angles between the bases add up to 180\u00b0<\/strong>.<\/p>\n\n\n\nSo:<\/p>\n\n\n\n
- \n
- \u2220D + \u2220G = 180\u00b0<\/li>\n\n\n\n
- \u2220D + 62\u00b0 = 180\u00b0<\/li>\n\n\n\n
- \u2220D = 180\u00b0 – 62\u00b0 = 118\u00b0<\/strong><\/li>\n<\/ul>\n\n\n\n
Final Answer:<\/h3>\n\n\n\n
B. 118\u00b0<\/strong><\/p>\n\n\n\n
\n\n\n\nExplanation:<\/h3>\n\n\n\n
In this geometry problem, we\u2019re asked to determine the measure of angle D in an isosceles trapezoid DEFG. The key features of an isosceles trapezoid are that it has one pair of parallel sides (the bases), and the non-parallel sides (legs) are of equal length. This symmetry also means that the angles at each base are equal in measure.<\/p>\n\n\n\n
When you\u2019re given that one of the angles is 62\u00b0, and DEFG is isosceles, then its corresponding angle on the same base must also be 62\u00b0. These are called the base angles. For example, if \u2220F is 62\u00b0, then \u2220G must also be 62\u00b0.<\/p>\n\n\n\n
Next, since the trapezoid\u2019s bases are parallel, and the legs connect these bases, each leg forms a pair of supplementary angles<\/strong> with the bases. That means \u2220D and \u2220G are on the same leg, and must add up to 180\u00b0. This is a property of trapezoids because the interior angles along a transversal between two parallel lines are supplementary.<\/p>\n\n\n\n
Given that \u2220G is 62\u00b0, then:<\/p>\n\n\n\n
- \n
- \u2220D + \u2220G = 180\u00b0<\/li>\n\n\n\n
- \u2220D = 180\u00b0 – 62\u00b0 = 118\u00b0<\/li>\n<\/ul>\n\n\n\n
Therefore, the measure of \u2220D is 118\u00b0. Understanding how angle relationships work in trapezoids\u2014especially isosceles trapezoids\u2014helps to find unknown angles quickly. The use of base angle congruency and the supplementary relationship between adjacent angles on a leg is essential to solving problems like this.<\/p>\n\n\n\n
\u2714\ufe0f Correct Answer: B. 118\u00b0<\/strong>.<\/p>\n\n\n\n
![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-79.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"5.6.3 Quiz: Trapezoids 2 Points DEFG is an isosceles trapezoid. Find the measure of 118\u00b0 D A. 72\u00b0 B. 118\u00b0 C. 28\u00b0 D. 62\u00b0 ? PREVIOUS G F 62\u00b0 SUBMIT The Correct Answer and Explanation is: To solve this problem, we are given: Step-by-Step Solution Step 1: Understanding an isosceles trapezoid An isosceles trapezoid is […]<\/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-230680","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230680","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=230680"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230680\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=230680"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=230680"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=230680"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
- If \u2220F<\/strong> and \u2220G<\/strong> are on the other base (say base FG<\/strong>), then \u2220F \u2245 \u2220G.<\/li>\n<\/ul>\n\n\n\n
- One angle is 118\u00b0<\/strong><\/li>\n\n\n\n