{"id":279900,"date":"2025-08-04T12:24:59","date_gmt":"2025-08-04T12:24:59","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=279900"},"modified":"2025-08-04T12:25:03","modified_gmt":"2025-08-04T12:25:03","slug":"figure-abcd-is-a-parallelogram","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/08\/04\/figure-abcd-is-a-parallelogram\/","title":{"rendered":"Figure ABCD is a parallelogram"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/08\/image-368.png\" alt=\"\" class=\"wp-image-279901\"\/><\/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>The correct value of p is 6.<\/p>\n\n\n\n<p>To determine the value of p, we need to use the properties of a parallelogram. A key property of a parallelogram is that its opposite sides are parallel. In the given figure ABCD, this means that side AB is parallel to side DC.<\/p>\n\n\n\n<p>The line segment AC acts as a transversal that intersects these two parallel lines, AB and DC. When a transversal intersects two parallel lines, it creates pairs of angles with special relationships. The two angles given in the problem are \u2220BAC, with a measure of (4p + 12) degrees, and \u2220ACD, with a measure of 36 degrees.<\/p>\n\n\n\n<p>These two angles are located on opposite sides of the transversal AC and are situated between the parallel lines AB and DC. This specific arrangement means they are alternate interior angles. A fundamental theorem in geometry states that alternate interior angles formed by a transversal cutting across parallel lines are equal in measure.<\/p>\n\n\n\n<p>Therefore, we can set the expressions for the measures of \u2220BAC and \u2220ACD equal to each other to form an algebraic equation:<\/p>\n\n\n\n<p>Measure of \u2220BAC = Measure of \u2220ACD<br>4p + 12 = 36<\/p>\n\n\n\n<p>Now, we can solve this equation for p. First, we isolate the term with p by subtracting 12 from both sides of the equation:<\/p>\n\n\n\n<p>4p + 12 &#8211; 12 = 36 &#8211; 12<br>4p = 24<\/p>\n\n\n\n<p>Next, to find the value of p, we divide both sides of the equation by 4:<\/p>\n\n\n\n<p>4p \/ 4 = 24 \/ 4<br>p = 6<\/p>\n\n\n\n<p>Thus, the value of p is 6. This corresponds to the first choice in the list of options. By correctly identifying the figure as a parallelogram and applying the property of equal alternate interior angles, we can solve for the unknown variable.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/08\/learnexams-banner5-227.jpeg\" alt=\"\" class=\"wp-image-279902\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The Correct Answer and Explanation is: The correct value of p is 6. To determine the value of p, we need to use the properties of a parallelogram. A key property of a parallelogram is that its opposite sides are parallel. In the given figure ABCD, this means that side AB is parallel to side [&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-279900","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/279900","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=279900"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/279900\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=279900"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=279900"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=279900"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}