{"id":237722,"date":"2025-06-17T13:44:33","date_gmt":"2025-06-17T13:44:33","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=237722"},"modified":"2025-06-17T13:44:35","modified_gmt":"2025-06-17T13:44:35","slug":"an-inscribed-quadrilateral-in-a-circle-is-shown-which-statements-are-correct","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/17\/an-inscribed-quadrilateral-in-a-circle-is-shown-which-statements-are-correct\/","title":{"rendered":"An inscribed quadrilateral in a circle is shown, which statements are correct"},"content":{"rendered":"\n<p>5) A (4y +14)^ 105^ C (7y+1)^ (7x+1)^ B An inscribed quadrilateral in a circle is shown, which statements are correct? 4))) A) x = 13^ B) y = 15^ C) \\angle A = 74^ D) \\angle B = 75^ E) \\angle C = 108^<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/image-657.png\" alt=\"\" class=\"wp-image-237723\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To solve this, we analyze the properties of an <strong>inscribed quadrilateral<\/strong> in a circle.<\/p>\n\n\n\n<p><strong>Key Property:<\/strong><br>In a cyclic quadrilateral (a quadrilateral inscribed in a circle), the opposite angles are <strong>supplementary<\/strong>, meaning they add up to 180\u00b0.<\/p>\n\n\n\n<p>From the image, we are given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u2220C = 105\u00b0<\/li>\n\n\n\n<li>\u2220A = (4y + 14)\u00b0<\/li>\n\n\n\n<li>\u2220B = (7x + 1)\u00b0<\/li>\n\n\n\n<li>\u2220D = (7y + 1)\u00b0<\/li>\n<\/ul>\n\n\n\n<p>Let\u2019s now apply the rule about opposite angles.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Use \u2220A + \u2220C = 180\u00b0<\/h3>\n\n\n\n<p>(4y+14)+105=180\u21d24y+119=180\u21d24y=61\u21d2y=15.25(4y + 14) + 105 = 180 \\Rightarrow 4y + 119 = 180 \\Rightarrow 4y = 61 \\Rightarrow y = 15.25(4y+14)+105=180\u21d24y+119=180\u21d24y=61\u21d2y=15.25<\/p>\n\n\n\n<p>This is not equal to <strong>15<\/strong>, so <strong>option B is incorrect<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Use \u2220B + \u2220D = 180\u00b0<\/h3>\n\n\n\n<p>(7x+1)+(7y+1)=180\u21d27x+7y+2=180(7x + 1) + (7y + 1) = 180 \\Rightarrow 7x + 7y + 2 = 180(7x+1)+(7y+1)=180\u21d27x+7y+2=180<\/p>\n\n\n\n<p>Now substitute y=15.25y = 15.25y=15.25:7x+7(15.25)+2=1807x+106.75+2=1807x=180\u2212108.75=71.25x=10.187x + 7(15.25) + 2 = 180 \\\\ 7x + 106.75 + 2 = 180 \\\\ 7x = 180 &#8211; 108.75 = 71.25 \\\\ x = 10.187x+7(15.25)+2=1807x+106.75+2=1807x=180\u2212108.75=71.25x=10.18<\/p>\n\n\n\n<p>So <strong>x \u2260 13<\/strong>, meaning <strong>option A is incorrect<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Calculate angles using values<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u2220A = 4y + 14 = 4(15.25) + 14 = 61 + 14 = <strong>75\u00b0<\/strong><\/li>\n\n\n\n<li>\u2220B = 7x + 1 = 7(10.18) + 1 \u2248 71.26 + 1 = <strong>72.26\u00b0<\/strong><\/li>\n\n\n\n<li>\u2220C = given as <strong>105\u00b0<\/strong><\/li>\n\n\n\n<li>\u2220D = 7y + 1 = 7(15.25) + 1 = 106.75 + 1 = <strong>107.75\u00b0<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Check the options:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>C) \u2220A = 74\u00b0 \u2192 False<\/li>\n\n\n\n<li>D) \u2220B = 75\u00b0 \u2192 False<\/li>\n\n\n\n<li>E) \u2220C = 108\u00b0 \u2192 False<\/li>\n<\/ul>\n\n\n\n<p>None of the options match the calculated values exactly. However, \u2220D (107.75\u00b0) and given \u2220C (105\u00b0) are supplementary to angles very close to \u2220A and \u2220B, respectively.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p><strong>None of the options are exactly correct<\/strong>, but the <strong>closest correct statement<\/strong> is:<\/p>\n\n\n\n<p><strong>\u2220A = 75\u00b0<\/strong>, which makes <strong>option D<\/strong> very close, but not exact.<br><strong>Correct answer: None of the given statements are entirely correct.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-908.jpeg\" alt=\"\" class=\"wp-image-237724\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>5) A (4y +14)^ 105^ C (7y+1)^ (7x+1)^ B An inscribed quadrilateral in a circle is shown, which statements are correct? 4))) A) x = 13^ B) y = 15^ C) \\angle A = 74^ D) \\angle B = 75^ E) \\angle C = 108^ The Correct Answer and Explanation is: To solve this, we [&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 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