{"id":265254,"date":"2025-07-21T19:53:51","date_gmt":"2025-07-21T19:53:51","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=265254"},"modified":"2025-07-21T19:53:53","modified_gmt":"2025-07-21T19:53:53","slug":"a-quadrilateral-can-be-constructed-with-four-obtuse-angles","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/21\/a-quadrilateral-can-be-constructed-with-four-obtuse-angles\/","title":{"rendered":"A quadrilateral can be constructed with four obtuse angles"},"content":{"rendered":"\n

A quadrilateral can be constructed with four obtuse angles. True False<\/p>\n\n\n\n

The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The correct answer is False<\/strong>.<\/p>\n\n\n\n

A quadrilateral is a polygon with four sides, and the sum of the interior angles of any quadrilateral is always 360 degrees. An obtuse angle is one that measures greater than 90 degrees but less than 180 degrees. If a quadrilateral were to have four obtuse angles, the total sum of the interior angles would exceed 360 degrees, which is impossible for a quadrilateral.<\/p>\n\n\n\n

Here\u2019s why:<\/p>\n\n\n\n

    \n
  1. Angle Sum of Quadrilaterals<\/strong>: The sum of the interior angles of any quadrilateral is 360 degrees. This is true regardless of the type of quadrilateral. The general formula for the sum of interior angles in any polygon is given by the equation: Sum\u00a0of\u00a0Interior\u00a0Angles=(n\u22122)\u00d7180\\text{Sum of Interior Angles} = (n – 2) \\times 180 where nn is the number of sides. For a quadrilateral (n=4n = 4): (4\u22122)\u00d7180=360\u2009degrees.(4 – 2) \\times 180 = 360 \\, \\text{degrees}.<\/li>\n\n\n\n
  2. Obtuse Angles<\/strong>: An obtuse angle is one that measures between 90 and 180 degrees. If a quadrilateral were to have four obtuse angles, the sum would be: 4\u00d791=364\u2009degrees\u00a0(minimum\u00a0sum\u00a0of\u00a0four\u00a0obtuse\u00a0angles).4 \\times 91 = 364 \\, \\text{degrees (minimum sum of four obtuse angles)}. This is already more than 360 degrees, which is not possible because it violates the basic rule of geometry that the sum of the interior angles of a quadrilateral must equal 360 degrees.<\/li>\n<\/ol>\n\n\n\n

    Thus, it is geometrically impossible for a quadrilateral to have four obtuse angles.<\/p>\n","protected":false},"excerpt":{"rendered":"

    A quadrilateral can be constructed with four obtuse angles. True False The correct answer and explanation is: The correct answer is False. A quadrilateral is a polygon with four sides, and the sum of the interior angles of any quadrilateral is always 360 degrees. An obtuse angle is one that measures greater than 90 degrees […]<\/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-265254","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/265254","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=265254"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/265254\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=265254"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=265254"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=265254"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}