{"id":262816,"date":"2025-07-20T19:16:23","date_gmt":"2025-07-20T19:16:23","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=262816"},"modified":"2025-07-20T19:16:26","modified_gmt":"2025-07-20T19:16:26","slug":"determine-the-value-of-x-in-the-diagram-x","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/20\/determine-the-value-of-x-in-the-diagram-x\/","title":{"rendered":"Determine the value of x in the diagram X"},"content":{"rendered":"\n

Determine the value of x in the diagram X<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Correct Answer:<\/strong>
x = 144<\/p>\n\n\n\n

Explanation:<\/strong><\/p>\n\n\n\n

    \n
  1. Identify the Shape and its Properties:<\/strong>
    The diagram shows a quadrilateral with two pairs of parallel sides, indicated by the arrow markings. A quadrilateral with two pairs of parallel sides is a parallelogram. A key property of a parallelogram is that its consecutive interior angles are supplementary, meaning they add up to 180 degrees. Also, opposite angles are equal.<\/li>\n\n\n\n
  2. Analyze the Angles:<\/strong>
    The diagram provides expressions for the angles in terms of a variable\u00a0x.\n
      \n
    • One interior angle is given as\u00a0x\u00b0.<\/li>\n\n\n\n
    • Another angle is given as\u00a0(x\/4)\u00b0. This value is used to label an exterior angle, which is vertically opposite to an interior angle. This means one of the interior angles of the parallelogram is\u00a0(x\/4)\u00b0.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • Set Up the Equation:<\/strong>
      In a parallelogram, there are two pairs of equal angles. The angles\u00a0x\u00b0\u00a0and\u00a0(x\/4)\u00b0\u00a0are clearly intended to be the two different angle measures in the parallelogram. As seen in the diagram, one angle (x\u00b0) is obtuse (greater than 90\u00b0) and the other ((x\/4)\u00b0) is acute (less than 90\u00b0). These must be consecutive angles.Since consecutive angles in a parallelogram are supplementary, we can set up the following equation:
      x + x\/4 = 180<\/li>\n\n\n\n
    • Solve the Equation for x:<\/strong>
      To solve for\u00a0x, we first need to combine the terms on the left side of the equation.\n
        \n
      • Find a common denominator:\u00a0(4x\/4) + (x\/4) = 180<\/li>\n\n\n\n
      • Add the fractions:\u00a05x\/4 = 180<\/li>\n\n\n\n
      • To isolate\u00a0x, multiply both sides by 4:\u00a05x = 180 * 4<\/li>\n\n\n\n
      • 5x = 720<\/li>\n\n\n\n
      • Finally, divide both sides by 5:\u00a0x = 720 \/ 5<\/li>\n\n\n\n
      • x = 144<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n

        Conclusion:<\/strong>
        The value of x is 144. This means the two consecutive angles of the parallelogram are 144\u00b0 and (144\/4)\u00b0 = 36\u00b0. Their sum is 144\u00b0 + 36\u00b0 = 180\u00b0, which confirms our use of the supplementary angles property.<\/p>\n\n\n\n

        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

        Determine the value of x in the diagram X The Correct Answer and Explanation is: Correct Answer:x = 144 Explanation: Conclusion:The value of x is 144. This means the two consecutive angles of the parallelogram are 144\u00b0 and (144\/4)\u00b0 = 36\u00b0. Their sum is 144\u00b0 + 36\u00b0 = 180\u00b0, which confirms our use of the […]<\/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-262816","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/262816","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=262816"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/262816\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=262816"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=262816"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=262816"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}