{"id":234795,"date":"2025-06-14T13:08:24","date_gmt":"2025-06-14T13:08:24","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=234795"},"modified":"2025-06-14T13:08:26","modified_gmt":"2025-06-14T13:08:26","slug":"triangle-fgh-is-a-right-triangle-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/14\/triangle-fgh-is-a-right-triangle-2\/","title":{"rendered":"Triangle FGH is a right triangle."},"content":{"rendered":"\n<p>Triangle FGH is a right triangle. Angle G is a right angle, m\u2220F = 9x \u2013 1, and m\u2220H = 3x + 7. What is m\u2220F?<\/p>\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>In a triangle, the sum of the interior angles is always 180 degrees. Since triangle FGH is a <strong>right triangle<\/strong> and angle G is the <strong>right angle<\/strong>, angle G measures <strong>90 degrees<\/strong>.<\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u2220G = 90\u00b0<\/li>\n\n\n\n<li>m\u2220F = 9x \u2013 1<\/li>\n\n\n\n<li>m\u2220H = 3x + 7<\/li>\n<\/ul>\n\n\n\n<p>To find the value of <strong>x<\/strong>, use the fact that:<br><br>m\u2220F + m\u2220H = 90\u00b0 (since the other 90\u00b0 is taken by the right angle)<\/p>\n\n\n\n<p>So:<br><br>(9x \u2013 1) + (3x + 7) = 90<\/p>\n\n\n\n<p>Simplify the left-hand side:<br><br>9x \u2013 1 + 3x + 7 = 90<br>12x + 6 = 90<\/p>\n\n\n\n<p>Subtract 6 from both sides:<br><br>12x = 84<\/p>\n\n\n\n<p>Divide both sides by 12:<br><br>x = 7<\/p>\n\n\n\n<p>Now substitute <strong>x = 7<\/strong> into the expression for m\u2220F:<\/p>\n\n\n\n<p>m\u2220F = 9x \u2013 1<br>m\u2220F = 9(7) \u2013 1<br>m\u2220F = 63 \u2013 1<br>m\u2220F = <strong>62\u00b0<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Explanation (300 words):<\/strong><\/p>\n\n\n\n<p>Triangles are fundamental shapes in geometry, each having three angles whose measures always add up to 180 degrees. In a <strong>right triangle<\/strong>, one of these angles measures exactly 90 degrees. The two remaining angles must then sum up to 90 degrees to maintain the total sum of 180 degrees.<\/p>\n\n\n\n<p>Triangle FGH is labeled as a right triangle, with angle G specified as the right angle. That leaves angles F and H as the two acute angles. The measures of these angles are given in terms of a variable <strong>x<\/strong>: angle F is expressed as <strong>9x \u2013 1<\/strong> and angle H as <strong>3x + 7<\/strong>. Since the right angle at G takes up 90 degrees, angles F and H together must also add up to 90 degrees.<\/p>\n\n\n\n<p>By combining the expressions for angle F and angle H and setting their sum equal to 90 degrees, it becomes possible to form a simple algebraic equation: (9x \u2013 1) + (3x + 7) = 90. Solving this equation reveals the value of <strong>x<\/strong>, which turns out to be <strong>7<\/strong>. This value is then substituted back into the expression for angle F, yielding <strong>m\u2220F = 62\u00b0<\/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-banner8-496.jpeg\" alt=\"\" class=\"wp-image-234796\"\/><\/figure>\n\n\n\n<p>This process demonstrates how algebra and geometric properties work together to solve unknown angle measures in a triangle. Recognizing the relationships among angles in right triangles is essential in both pure mathematics and applied settings like construction, navigation, and design.<\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Triangle FGH is a right triangle. Angle G is a right angle, m\u2220F = 9x \u2013 1, and m\u2220H = 3x + 7. What is m\u2220F? The Correct Answer and Explanation is: In a triangle, the sum of the interior angles is always 180 degrees. Since triangle FGH is a right triangle and angle G [&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-234795","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/234795","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=234795"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/234795\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=234795"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=234795"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=234795"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}