{"id":4465,"date":"2023-01-29T10:00:25","date_gmt":"2023-01-29T04:30:25","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=4465"},"modified":"2023-01-30T10:03:09","modified_gmt":"2023-01-30T04:33:09","slug":"convex-concave-angle-sum-property-of-quadrilaterals","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/convex-concave-angle-sum-property-of-quadrilaterals\/","title":{"rendered":"Convex and Concave Quadrilaterals"},"content":{"rendered":"<h2><strong>Convex and Concave <a href=\"https:\/\/www.aplustopper.com\/what-is-a-quadrilateral\/\">Quadrilaterals<\/a><\/strong><\/h2>\n<p><strong>Convex quadrilateral:<\/strong> A quadrilateral is called a convex quadrilateral, if the line segment joining any two vertices of the quadrilateral is in the same region.<br \/>\nIn figure, ABCD is a convex quadrilateral because AB, BC, CD, DA, AC, BD are in the same region of the quadrilateral.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/c1.staticflickr.com\/9\/8445\/29957363751_83eaa50222_o.png\" alt=\"Convex-Quadrilateral\" width=\"236\" height=\"164\" \/>In a convex quadrilateral each angle measures less than 180\u00b0.<\/p>\n<p><strong>Concave quadrilateral:<\/strong> A quadrilateral is called a concave quadrilateral, if at least one line segment joining the vertices is not a part of the same region of the quadrilateral.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/c2.staticflickr.com\/6\/5229\/30006817306_9af45fcbd5_o.png\" alt=\"Concave-Quadrilateral\" width=\"248\" height=\"140\" \/>That is, any line segment that joins two interior points goes outside the figure. In a concave quadrilateral at least one angle is a reflex angle, i.e., an angle larger than 180\u00b0.\u00a0In figure, ABCD is a concave quadrilateral because a line joining the vertices A and C is going outside the quadrilateral region.<\/p>\n<h2><strong>Angle sum property of a quadrilateral<\/strong><\/h2>\n<p>The sum of all angles of a quadrilateral is 360\u00b0 or four right angles.<br \/>\nDraw a quadrilateral ABCD with one of its diagonals AC.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/c1.staticflickr.com\/9\/8592\/29957417191_ef7b95a91b_o.png\" alt=\"Angle-sum-property-quadrilateral\" width=\"255\" height=\"215\" \/><br \/>\nDiagonal AC divides the quadrilateral into two triangles, i.e., \u0394ADC and \u0394ABC.<br \/>\nClearly \u2220l + \u22202 = \u2220A<br \/>\nand \u22203 + \u22204 = \u2220C \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0&#8230;(1)<br \/>\nWe know that the sum of the angles of a triangle is 180\u00b0.<br \/>\n\u2234 In \u0394ABC, \u22201 + \u22203 + \u2220B = 180\u00b0<br \/>\nIn \u0394ADC, \u22202 + \u22204 + \u2220D = 180\u00b0<br \/>\nSum of the angles of a quadrilateral<br \/>\n= Sum of the angles of \u0394ABC and \u0394ADC<br \/>\n\u2234 (\u22201 + \u22203 + \u2220B) + (\u22202 + \u22204 + \u2220D)\u00a0= 180\u00b0 + 180\u00b0<br \/>\nor \u22201 + \u22203 + \u2220B + \u22202 + \u22204 + \u2220D = 360\u00b0<br \/>\nor (\u22201 + \u22202) + \u2220B + (\u22203 + \u22204) + \u2220D = 360\u00b0<br \/>\nor \u2220A + \u2220B + \u2220C + \u2220D = 360\u00b0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0(using 1)<br \/>\nHence, the sum of the angles of a quadrilateral equals 360\u00b0.<\/p>\n<p><strong>Example 1:<\/strong> The angles of a quadrilateral are in the ratio of 1 : 2 : 1 : 2. Find the measure of each angle.<br \/>\n<strong>Solution:<\/strong> Let the first angle of a quadrilateral be x.<br \/>\nHere, second angle = 2x<br \/>\nthird angle = x<br \/>\nfourth angle = 2x<br \/>\nSum of all angles of a quadrilateral = 360\u00b0<br \/>\n\u2234 x + 2x + x + 2x = 360\u00b0<br \/>\n6x = 360\u00b0<br \/>\nx\u00a0= 60\u00b0<br \/>\n\u2234 First angle = x = 60\u00b0<br \/>\nSecond angle = 2x = 2 \u00d7\u00a060\u00b0 = 120\u00b0<br \/>\nThird angle = x = 60\u00b0<br \/>\nFourth angle = 2x = 120\u00b0.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Convex and Concave Quadrilaterals Convex quadrilateral: A quadrilateral is called a convex quadrilateral, if the line segment joining any two vertices of the quadrilateral is in the same region. In figure, ABCD is a convex quadrilateral because AB, BC, CD, DA, AC, BD are in the same region of the quadrilateral. In a convex quadrilateral [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[5],"tags":[2492,2491,2489,2490,2483],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.8 (Yoast SEO v17.8) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Convex and Concave Quadrilaterals - A Plus Topper<\/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:\/\/www.aplustopper.com\/convex-concave-angle-sum-property-of-quadrilaterals\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Convex and Concave Quadrilaterals\" \/>\n<meta property=\"og:description\" content=\"Convex and Concave Quadrilaterals Convex quadrilateral: A quadrilateral is called a convex quadrilateral, if the line segment joining any two vertices of the quadrilateral is in the same region. In figure, ABCD is a convex quadrilateral because AB, BC, CD, DA, AC, BD are in the same region of the quadrilateral. In a convex quadrilateral [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.aplustopper.com\/convex-concave-angle-sum-property-of-quadrilaterals\/\" \/>\n<meta property=\"og:site_name\" content=\"A Plus Topper\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/aplustopper\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-01-29T04:30:25+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-01-30T04:33:09+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/c1.staticflickr.com\/9\/8445\/29957363751_83eaa50222_o.png\" \/>\n<meta name=\"twitter:card\" content=\"summary\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Veerendra\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Organization\",\"@id\":\"https:\/\/www.aplustopper.com\/#organization\",\"name\":\"Aplus Topper\",\"url\":\"https:\/\/www.aplustopper.com\/\",\"sameAs\":[\"https:\/\/www.facebook.com\/aplustopper\/\"],\"logo\":{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/www.aplustopper.com\/#logo\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg\",\"contentUrl\":\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg\",\"width\":1585,\"height\":375,\"caption\":\"Aplus Topper\"},\"image\":{\"@id\":\"https:\/\/www.aplustopper.com\/#logo\"}},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.aplustopper.com\/#website\",\"url\":\"https:\/\/www.aplustopper.com\/\",\"name\":\"A Plus Topper\",\"description\":\"Improve your Grades\",\"publisher\":{\"@id\":\"https:\/\/www.aplustopper.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/www.aplustopper.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/www.aplustopper.com\/convex-concave-angle-sum-property-of-quadrilaterals\/#primaryimage\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/c1.staticflickr.com\/9\/8445\/29957363751_83eaa50222_o.png\",\"contentUrl\":\"https:\/\/c1.staticflickr.com\/9\/8445\/29957363751_83eaa50222_o.png\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.aplustopper.com\/convex-concave-angle-sum-property-of-quadrilaterals\/#webpage\",\"url\":\"https:\/\/www.aplustopper.com\/convex-concave-angle-sum-property-of-quadrilaterals\/\",\"name\":\"Convex and Concave Quadrilaterals - A Plus Topper\",\"isPartOf\":{\"@id\":\"https:\/\/www.aplustopper.com\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/www.aplustopper.com\/convex-concave-angle-sum-property-of-quadrilaterals\/#primaryimage\"},\"datePublished\":\"2023-01-29T04:30:25+00:00\",\"dateModified\":\"2023-01-30T04:33:09+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/www.aplustopper.com\/convex-concave-angle-sum-property-of-quadrilaterals\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/www.aplustopper.com\/convex-concave-angle-sum-property-of-quadrilaterals\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/www.aplustopper.com\/convex-concave-angle-sum-property-of-quadrilaterals\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/www.aplustopper.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Convex and Concave Quadrilaterals\"}]},{\"@type\":\"Article\",\"@id\":\"https:\/\/www.aplustopper.com\/convex-concave-angle-sum-property-of-quadrilaterals\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/www.aplustopper.com\/convex-concave-angle-sum-property-of-quadrilaterals\/#webpage\"},\"author\":{\"@id\":\"https:\/\/www.aplustopper.com\/#\/schema\/person\/1363657f2432a17193a1f5d6404b8a0e\"},\"headline\":\"Convex and Concave Quadrilaterals\",\"datePublished\":\"2023-01-29T04:30:25+00:00\",\"dateModified\":\"2023-01-30T04:33:09+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/www.aplustopper.com\/convex-concave-angle-sum-property-of-quadrilaterals\/#webpage\"},\"wordCount\":313,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/www.aplustopper.com\/#organization\"},\"image\":{\"@id\":\"https:\/\/www.aplustopper.com\/convex-concave-angle-sum-property-of-quadrilaterals\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/c1.staticflickr.com\/9\/8445\/29957363751_83eaa50222_o.png\",\"keywords\":[\"Angle sum property of a quadrilateral\",\"Concave Quadrilaterals\",\"Convex and Concave Quadrilaterals\",\"Convex Quadrilaterals\",\"Quadrilateral\"],\"articleSection\":[\"Mathematics\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/www.aplustopper.com\/convex-concave-angle-sum-property-of-quadrilaterals\/#respond\"]}]},{\"@type\":\"Person\",\"@id\":\"https:\/\/www.aplustopper.com\/#\/schema\/person\/1363657f2432a17193a1f5d6404b8a0e\",\"name\":\"Veerendra\",\"image\":{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/www.aplustopper.com\/#personlogo\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/93ba5dedf76e89af65ae2e1d6ac09855?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/93ba5dedf76e89af65ae2e1d6ac09855?s=96&d=mm&r=g\",\"caption\":\"Veerendra\"},\"url\":\"https:\/\/www.aplustopper.com\/author\/veerendra\/\"}]}<\/script>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Convex and Concave Quadrilaterals - A Plus Topper","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:\/\/www.aplustopper.com\/convex-concave-angle-sum-property-of-quadrilaterals\/","og_locale":"en_US","og_type":"article","og_title":"Convex and Concave Quadrilaterals","og_description":"Convex and Concave Quadrilaterals Convex quadrilateral: A quadrilateral is called a convex quadrilateral, if the line segment joining any two vertices of the quadrilateral is in the same region. In figure, ABCD is a convex quadrilateral because AB, BC, CD, DA, AC, BD are in the same region of the quadrilateral. In a convex quadrilateral [&hellip;]","og_url":"https:\/\/www.aplustopper.com\/convex-concave-angle-sum-property-of-quadrilaterals\/","og_site_name":"A Plus Topper","article_publisher":"https:\/\/www.facebook.com\/aplustopper\/","article_published_time":"2023-01-29T04:30:25+00:00","article_modified_time":"2023-01-30T04:33:09+00:00","og_image":[{"url":"https:\/\/c1.staticflickr.com\/9\/8445\/29957363751_83eaa50222_o.png"}],"twitter_card":"summary","twitter_misc":{"Written by":"Veerendra","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/www.aplustopper.com\/#organization","name":"Aplus Topper","url":"https:\/\/www.aplustopper.com\/","sameAs":["https:\/\/www.facebook.com\/aplustopper\/"],"logo":{"@type":"ImageObject","@id":"https:\/\/www.aplustopper.com\/#logo","inLanguage":"en-US","url":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg","contentUrl":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg","width":1585,"height":375,"caption":"Aplus Topper"},"image":{"@id":"https:\/\/www.aplustopper.com\/#logo"}},{"@type":"WebSite","@id":"https:\/\/www.aplustopper.com\/#website","url":"https:\/\/www.aplustopper.com\/","name":"A Plus Topper","description":"Improve your Grades","publisher":{"@id":"https:\/\/www.aplustopper.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.aplustopper.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"ImageObject","@id":"https:\/\/www.aplustopper.com\/convex-concave-angle-sum-property-of-quadrilaterals\/#primaryimage","inLanguage":"en-US","url":"https:\/\/c1.staticflickr.com\/9\/8445\/29957363751_83eaa50222_o.png","contentUrl":"https:\/\/c1.staticflickr.com\/9\/8445\/29957363751_83eaa50222_o.png"},{"@type":"WebPage","@id":"https:\/\/www.aplustopper.com\/convex-concave-angle-sum-property-of-quadrilaterals\/#webpage","url":"https:\/\/www.aplustopper.com\/convex-concave-angle-sum-property-of-quadrilaterals\/","name":"Convex and Concave Quadrilaterals - A Plus Topper","isPartOf":{"@id":"https:\/\/www.aplustopper.com\/#website"},"primaryImageOfPage":{"@id":"https:\/\/www.aplustopper.com\/convex-concave-angle-sum-property-of-quadrilaterals\/#primaryimage"},"datePublished":"2023-01-29T04:30:25+00:00","dateModified":"2023-01-30T04:33:09+00:00","breadcrumb":{"@id":"https:\/\/www.aplustopper.com\/convex-concave-angle-sum-property-of-quadrilaterals\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.aplustopper.com\/convex-concave-angle-sum-property-of-quadrilaterals\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/www.aplustopper.com\/convex-concave-angle-sum-property-of-quadrilaterals\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/www.aplustopper.com\/"},{"@type":"ListItem","position":2,"name":"Convex and Concave Quadrilaterals"}]},{"@type":"Article","@id":"https:\/\/www.aplustopper.com\/convex-concave-angle-sum-property-of-quadrilaterals\/#article","isPartOf":{"@id":"https:\/\/www.aplustopper.com\/convex-concave-angle-sum-property-of-quadrilaterals\/#webpage"},"author":{"@id":"https:\/\/www.aplustopper.com\/#\/schema\/person\/1363657f2432a17193a1f5d6404b8a0e"},"headline":"Convex and Concave Quadrilaterals","datePublished":"2023-01-29T04:30:25+00:00","dateModified":"2023-01-30T04:33:09+00:00","mainEntityOfPage":{"@id":"https:\/\/www.aplustopper.com\/convex-concave-angle-sum-property-of-quadrilaterals\/#webpage"},"wordCount":313,"commentCount":0,"publisher":{"@id":"https:\/\/www.aplustopper.com\/#organization"},"image":{"@id":"https:\/\/www.aplustopper.com\/convex-concave-angle-sum-property-of-quadrilaterals\/#primaryimage"},"thumbnailUrl":"https:\/\/c1.staticflickr.com\/9\/8445\/29957363751_83eaa50222_o.png","keywords":["Angle sum property of a quadrilateral","Concave Quadrilaterals","Convex and Concave Quadrilaterals","Convex Quadrilaterals","Quadrilateral"],"articleSection":["Mathematics"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/www.aplustopper.com\/convex-concave-angle-sum-property-of-quadrilaterals\/#respond"]}]},{"@type":"Person","@id":"https:\/\/www.aplustopper.com\/#\/schema\/person\/1363657f2432a17193a1f5d6404b8a0e","name":"Veerendra","image":{"@type":"ImageObject","@id":"https:\/\/www.aplustopper.com\/#personlogo","inLanguage":"en-US","url":"https:\/\/secure.gravatar.com\/avatar\/93ba5dedf76e89af65ae2e1d6ac09855?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/93ba5dedf76e89af65ae2e1d6ac09855?s=96&d=mm&r=g","caption":"Veerendra"},"url":"https:\/\/www.aplustopper.com\/author\/veerendra\/"}]}},"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/www.aplustopper.com\/wp-json\/wp\/v2\/posts\/4465"}],"collection":[{"href":"https:\/\/www.aplustopper.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.aplustopper.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.aplustopper.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.aplustopper.com\/wp-json\/wp\/v2\/comments?post=4465"}],"version-history":[{"count":1,"href":"https:\/\/www.aplustopper.com\/wp-json\/wp\/v2\/posts\/4465\/revisions"}],"predecessor-version":[{"id":155306,"href":"https:\/\/www.aplustopper.com\/wp-json\/wp\/v2\/posts\/4465\/revisions\/155306"}],"wp:attachment":[{"href":"https:\/\/www.aplustopper.com\/wp-json\/wp\/v2\/media?parent=4465"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.aplustopper.com\/wp-json\/wp\/v2\/categories?post=4465"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.aplustopper.com\/wp-json\/wp\/v2\/tags?post=4465"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}