- \n
- \u2220BAC and \u2220CAD<\/li>\n\n\n\n
- \u2220BAE and \u2220EAD<\/li>\n\n\n\n
- \u2220EAD and \u2220DAC<\/li>\n<\/ul>\n\n\n\n
\n\n\n\nExplanation<\/h3>\n\n\n\n
In geometry, a linear pair<\/strong> is a set of two angles that satisfy two specific conditions:<\/p>\n\n\n\n
- \n
- The angles must be\u00a0adjacent<\/strong>, meaning they share a common vertex and a common side but do not have any interior points in common.<\/li>\n\n\n\n
- Their non-common sides must be\u00a0opposite rays<\/strong>, meaning they form a straight line.<\/li>\n<\/ol>\n\n\n\n
A key consequence of this definition is that the measures of the angles in a linear pair always add up to 180 degrees.<\/p>\n\n\n\n
Let’s analyze the given geometric setup. We have two lines, one containing points C, A, and E, and the other containing points B, A, and D. They intersect at point A. This means that line CAE and line BAD are straight lines.<\/p>\n\n\n\n
We can now evaluate each pair of angles:<\/p>\n\n\n\n
- \n
- \u2220BAC and \u2220CAD:<\/strong>\u00a0These angles are adjacent because they share vertex A and the common side AC. Their non-common sides are ray AB and ray AD. Since points B, A, and D lie on a straight line, ray AB and ray AD are opposite rays. Thus,\u00a0\u2220BAC and \u2220CAD are a linear pair.<\/strong><\/li>\n\n\n\n
- \u2220BAE and \u2220EAD:<\/strong>\u00a0These angles are adjacent as they share vertex A and the common side AE. Their non-common sides are ray AB and ray AD, which we already identified as opposite rays forming the straight line BD. Therefore,\u00a0\u2220BAE and \u2220EAD are a linear pair.<\/strong><\/li>\n\n\n\n
- \u2220EAD and \u2220DAC:<\/strong>\u00a0These angles are adjacent, sharing vertex A and the common side AD. Their non-common sides are ray AE and ray AC. Since points C, A, and E lie on a straight line, ray AE and ray AC are opposite rays. Consequently,\u00a0\u2220EAD and \u2220DAC are a linear pair.<\/strong><\/li>\n\n\n\n
- \u2220DAE and \u2220EAD:<\/strong>\u00a0This is not a pair of two distinct angles. \u2220DAE and \u2220EAD represent the exact same angle, simply named with the points in a different order. An angle cannot form a linear pair with itself.<\/li>\n\n\n\n
- \u2220CAE and \u2220BAD:<\/strong>\u00a0These are not adjacent angles. While they share vertex A, they do not share a common side. In fact, both are straight angles formed by the intersecting lines. They cannot form a linear pair.<\/li>\n<\/ul>\n\n\n\n
![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-378.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"lines intersect at point A. One line contains points C, A, E and the other line contains points B, A, D. Which are linear pairs? Check all that apply. \u2220DAE and \u2220EAD \u2220BAC and \u2220CAD \u2220BAE and \u2220EAD \u2220EAD and \u2220DAC \u2220CAE and \u2220BAD Correct Answer Explanation In geometry, a linear pair is a set of two […]<\/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-233969","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233969","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=233969"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233969\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=233969"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=233969"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=233969"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
- \u2220BAE and \u2220EAD:<\/strong>\u00a0These angles are adjacent as they share vertex A and the common side AE. Their non-common sides are ray AB and ray AD, which we already identified as opposite rays forming the straight line BD. Therefore,\u00a0\u2220BAE and \u2220EAD are a linear pair.<\/strong><\/li>\n\n\n\n
- Their non-common sides must be\u00a0opposite rays<\/strong>, meaning they form a straight line.<\/li>\n<\/ol>\n\n\n\n
- The angles must be\u00a0adjacent<\/strong>, meaning they share a common vertex and a common side but do not have any interior points in common.<\/li>\n\n\n\n