{"id":11250,"date":"2022-06-29T16:12:52","date_gmt":"2022-06-29T10:42:52","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11250"},"modified":"2022-06-29T16:12:56","modified_gmt":"2022-06-29T10:42:56","slug":"abcd-is-a-cyclic-quadrilateral-as-shown-in-figure-find-the-angles-of-the-cyclic-quadrilateral","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/abcd-is-a-cyclic-quadrilateral-as-shown-in-figure-find-the-angles-of-the-cyclic-quadrilateral\/","title":{"rendered":"ABCD is a cyclic quadrilateral as shown in figure. Find the angles of the cyclic quadrilateral."},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>We know that the sum of opposite angles of cyclic quadrilateral is 180 degrees.<img decoding=\"async\" loading=\"lazy\" class=\" wp-image-11251 alignright\" src=\"https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/06\/linearequation3-7-8.jpeg?resize=172%2C182&#038;ssl=1\" alt=\"cyclic quadrialteral\" width=\"172\" height=\"182\" srcset=\"https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/06\/linearequation3-7-8.jpeg?resize=283%2C300&amp;ssl=1 283w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/06\/linearequation3-7-8.jpeg?resize=967%2C1024&amp;ssl=1 967w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/06\/linearequation3-7-8.jpeg?resize=768%2C813&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/06\/linearequation3-7-8.jpeg?resize=1451%2C1536&amp;ssl=1 1451w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/06\/linearequation3-7-8.jpeg?w=1700&amp;ssl=1 1700w\" sizes=\"(max-width: 172px) 100vw, 172px\" data-recalc-dims=\"1\" \/><\/p>\n<p>Angles A and C, Angles B and D form pairs of opposite angles in the given cyclic quadrilateral ABCD.<\/p>\n<p>\\(\\angle\\)A + \\(\\angle\\)C = 180\u00a0 \u00a0and\u00a0 \\(\\angle\\)B + \\(\\angle\\)D = 180<\/p>\n<p>\\(\\implies\\)\u00a0 (4y + 20) + 4x = 180\u00a0 \u00a0and\u00a0 \u00a0(3y &#8211; 5) + (7x + 5) = 180<\/p>\n<p>\\(\\implies\\)\u00a0 4x + 4y &#8211; 160 = 0\u00a0 \u00a0 \u00a0\\(\\implies\\) x + y &#8211; 40 = 0\u00a0 \u00a0 \u00a0 &#8230;&#8230;&#8230;&#8230;(1)<\/p>\n<p>and\u00a0 7x + 3y &#8211; 180 = 0\u00a0 \u00a0 \u00a0 \u00a0 \u00a0&#8230;&#8230;&#8230;&#8230;(2)<\/p>\n<p>Multiplying equation (1) by and subtracting from equation (2), we get<\/p>\n<p>4x &#8211; 60 = 0\u00a0 \u00a0 \u00a0 \\(\\implies\\)\u00a0 \u00a0 x = 15<\/p>\n<p>Put the value of x = 15 in equation (1), we get<\/p>\n<p>15 + y &#8211; 40 = 0\u00a0 \u00a0 \u00a0\\(\\implies\\)\u00a0 \u00a0y = 25<\/p>\n<p>Hence, \\(\\angle\\)A = 4y + 20 = <strong>120 degrees<\/strong><\/p>\n<p>\\(\\angle\\)B = 3y &#8211; 5 = <strong>70 degrees<\/strong><\/p>\n<p>\\(\\angle\\)C = 4x = <strong>60 degrees<\/strong><\/p>\n<p>\\(\\angle\\)D = 7x + 5 = <strong>110 degrees<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution : We know that the sum of opposite angles of cyclic quadrilateral is 180 degrees. Angles A and C, Angles B and D form pairs of opposite angles in the given cyclic quadrilateral ABCD. \\(\\angle\\)A + \\(\\angle\\)C = 180\u00a0 \u00a0and\u00a0 \\(\\angle\\)B + \\(\\angle\\)D = 180 \\(\\implies\\)\u00a0 (4y + 20) + 4x = 180\u00a0 \u00a0and\u00a0 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/abcd-is-a-cyclic-quadrilateral-as-shown-in-figure-find-the-angles-of-the-cyclic-quadrilateral\/\"> <span class=\"screen-reader-text\">ABCD is a cyclic quadrilateral as shown in figure. Find the angles of the cyclic quadrilateral.<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[911,43],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>ABCD is a cyclic quadrilateral as shown in figure. Find the angles of the cyclic quadrilateral. - Mathemerize<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/abcd-is-a-cyclic-quadrilateral-as-shown-in-figure-find-the-angles-of-the-cyclic-quadrilateral\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"ABCD is a cyclic quadrilateral as shown in figure. Find the angles of the cyclic quadrilateral. - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : We know that the sum of opposite angles of cyclic quadrilateral is 180 degrees. Angles A and C, Angles B and D form pairs of opposite angles in the given cyclic quadrilateral ABCD. (angle)A + (angle)C = 180\u00a0 \u00a0and\u00a0 (angle)B + (angle)D = 180 (implies)\u00a0 (4y + 20) + 4x = 180\u00a0 \u00a0and\u00a0 &hellip; ABCD is a cyclic quadrilateral as shown in figure. Find the angles of the cyclic quadrilateral. 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Find the angles of the cyclic quadrilateral. - Mathemerize","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathemerize.com\/abcd-is-a-cyclic-quadrilateral-as-shown-in-figure-find-the-angles-of-the-cyclic-quadrilateral\/","og_locale":"en_US","og_type":"article","og_title":"ABCD is a cyclic quadrilateral as shown in figure. Find the angles of the cyclic quadrilateral. - Mathemerize","og_description":"Solution : We know that the sum of opposite angles of cyclic quadrilateral is 180 degrees. Angles A and C, Angles B and D form pairs of opposite angles in the given cyclic quadrilateral ABCD. (angle)A + (angle)C = 180\u00a0 \u00a0and\u00a0 (angle)B + (angle)D = 180 (implies)\u00a0 (4y + 20) + 4x = 180\u00a0 \u00a0and\u00a0 &hellip; ABCD is a cyclic quadrilateral as shown in figure. Find the angles of the cyclic quadrilateral. 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