{"id":168908,"date":"2024-11-18T17:50:46","date_gmt":"2024-11-18T17:50:46","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=168908"},"modified":"2024-11-18T17:51:16","modified_gmt":"2024-11-18T17:51:16","slug":"the-interior-angles-of-the-hexagon-are-2x-1-2-xx-40-110-130-160","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/18\/the-interior-angles-of-the-hexagon-are-2x-1-2-xx-40-110-130-160\/","title":{"rendered":"The interior angles of the hexagon are 2x\u00b0, 1\/2 x\u00b0,x + 40\u00b0, 110\u00b0, 130\u00b0, 160\u00b0."},"content":{"rendered":"\n<p>The interior angles of the hexagon are 2x\u00b0, 1\/2 x\u00b0,x + 40\u00b0, 110\u00b0, 130\u00b0, 160\u00b0. Find the value of the smallest angle. [3 Marks]<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To solve for the smallest angle in the hexagon, we need to use the fact that the sum of the interior angles of any polygon is calculated by the formula:Sum&nbsp;of&nbsp;interior&nbsp;angles=(n\u22122)\u00d7180\u2218\\text{Sum of interior angles} = (n &#8211; 2) \\times 180^\\circSum&nbsp;of&nbsp;interior&nbsp;angles=(n\u22122)\u00d7180\u2218<\/p>\n\n\n\n<p>where nnn is the number of sides of the polygon. Since we are dealing with a hexagon, n=6n = 6n=6. So, the sum of the interior angles of a hexagon is:(6\u22122)\u00d7180\u2218=4\u00d7180\u2218=720\u2218(6 &#8211; 2) \\times 180^\\circ = 4 \\times 180^\\circ = 720^\\circ(6\u22122)\u00d7180\u2218=4\u00d7180\u2218=720\u2218<\/p>\n\n\n\n<p>Given that the interior angles of the hexagon are 2x\u22182x^\\circ2x\u2218, 12x\u2218\\frac{1}{2}x^\\circ21\u200bx\u2218, x+40\u2218x + 40^\\circx+40\u2218, 110\u2218110^\\circ110\u2218, 130\u2218130^\\circ130\u2218, and 160\u2218160^\\circ160\u2218, we can set up an equation to find the value of xxx:2x+12x+(x+40)+110+130+160=7202x + \\frac{1}{2}x + (x + 40) + 110 + 130 + 160 = 7202x+21\u200bx+(x+40)+110+130+160=720<\/p>\n\n\n\n<p>Now, let&#8217;s simplify this equation:2x+12x+x+40+110+130+160=7202x + \\frac{1}{2}x + x + 40 + 110 + 130 + 160 = 7202x+21\u200bx+x+40+110+130+160=720<\/p>\n\n\n\n<p>Combine like terms:(2x+12x+x)+(40+110+130+160)=720(2x + \\frac{1}{2}x + x) + (40 + 110 + 130 + 160) = 720(2x+21\u200bx+x)+(40+110+130+160)=720 (3x+12x)+440=720\\left( 3x + \\frac{1}{2}x \\right) + 440 = 720(3x+21\u200bx)+440=720<\/p>\n\n\n\n<p>To combine the terms with xxx, we convert 3x3x3x to a fraction:6&#215;2+1&#215;2=7&#215;2\\frac{6x}{2} + \\frac{1x}{2} = \\frac{7x}{2}26x\u200b+21x\u200b=27x\u200b<\/p>\n\n\n\n<p>So the equation becomes:7&#215;2+440=720\\frac{7x}{2} + 440 = 72027x\u200b+440=720<\/p>\n\n\n\n<p>Now, subtract 440 from both sides:7&#215;2=280\\frac{7x}{2} = 28027x\u200b=280<\/p>\n\n\n\n<p>Multiply both sides by 2:7x=5607x = 5607x=560<\/p>\n\n\n\n<p>Now, divide both sides by 7:x=80x = 80x=80<\/p>\n\n\n\n<p>Now that we have x=80\u2218x = 80^\\circx=80\u2218, we can substitute it back into the expressions for the angles:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The first angle is 2x=2(80)=160\u22182x = 2(80) = 160^\\circ2x=2(80)=160\u2218,<\/li>\n\n\n\n<li>The second angle is 12x=12(80)=40\u2218\\frac{1}{2}x = \\frac{1}{2}(80) = 40^\\circ21\u200bx=21\u200b(80)=40\u2218,<\/li>\n\n\n\n<li>The third angle is x+40=80+40=120\u2218x + 40 = 80 + 40 = 120^\\circx+40=80+40=120\u2218,<\/li>\n\n\n\n<li>The other angles are given as 110\u00b0, 130\u00b0, and 160\u00b0.<\/li>\n<\/ul>\n\n\n\n<p>Thus, the smallest angle is 40\u221840^\\circ40\u2218.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p>The smallest angle in the hexagon is 40\u221840^\\circ40\u2218.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The interior angles of the hexagon are 2x\u00b0, 1\/2 x\u00b0,x + 40\u00b0, 110\u00b0, 130\u00b0, 160\u00b0. Find the value of the smallest angle. [3 Marks] The Correct Answer and Explanation is: To solve for the smallest angle in the hexagon, we need to use the fact that the sum of the interior angles of any polygon [&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-168908","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168908","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=168908"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168908\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=168908"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=168908"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=168908"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}