{"id":245867,"date":"2025-07-06T14:12:55","date_gmt":"2025-07-06T14:12:55","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=245867"},"modified":"2025-07-06T14:12:57","modified_gmt":"2025-07-06T14:12:57","slug":"consider-the-regular-do-decagon-shown-below","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/06\/consider-the-regular-do-decagon-shown-below\/","title":{"rendered":"Consider the regular do-decagon shown below"},"content":{"rendered":"\n<p>Consider the regular do-decagon shown below: (a) How many lines of symmetry does the regular do-decagon have? Draw all of the lines of symmetry in the figure above. (b) Determine the angle of rotational symmetry for the regular do-decagon.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/image-235.png\" alt=\"\" class=\"wp-image-245869\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>Let&#8217;s break down your questions step by step:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">(a) Number of Lines of Symmetry in a Regular Do-Decagon<\/h3>\n\n\n\n<p>A regular do-decagon has 12 sides, and for any regular polygon, the number of lines of symmetry is equal to the number of sides. Thus, a regular do-decagon has 12 lines of symmetry. These lines can be drawn in two different ways:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Through opposite vertices<\/strong>: These lines will pass through pairs of opposite vertices, dividing the decagon into two symmetrical halves.<\/li>\n\n\n\n<li><strong>Through the midpoints of opposite sides<\/strong>: These lines will pass through the midpoints of opposite sides, dividing the decagon in a way that reflects each side into its counterpart.<\/li>\n<\/ol>\n\n\n\n<p>So, you can draw 12 lines of symmetry in total, ensuring each one is either through opposite vertices or through the midpoints of opposite sides.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">(b) Angle of Rotational Symmetry for the Regular Do-Decagon<\/h3>\n\n\n\n<p>The angle of rotational symmetry is the smallest angle by which the figure can be rotated such that it looks the same as it did before the rotation.<\/p>\n\n\n\n<p>For a regular do-decagon, which has 12 sides, the angle of rotational symmetry is calculated by dividing 360 degrees by the number of sides. This gives us:Angle&nbsp;of&nbsp;rotational&nbsp;symmetry=360\u221812=30\u2218\\text{Angle of rotational symmetry} = \\frac{360^\\circ}{12} = 30^\\circAngle&nbsp;of&nbsp;rotational&nbsp;symmetry=12360\u2218\u200b=30\u2218<\/p>\n\n\n\n<p>Therefore, the regular do-decagon has a rotational symmetry of 30 degrees. This means that rotating the do-decagon by multiples of 30 degrees (e.g., 30\u00b0, 60\u00b0, 90\u00b0, etc.) will map the shape onto itself.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Summary:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>(a)<\/strong> The regular do-decagon has 12 lines of symmetry.<\/li>\n\n\n\n<li><strong>(b)<\/strong> The angle of rotational symmetry is 30\u00b0.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-735.jpeg\" alt=\"\" class=\"wp-image-245868\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Consider the regular do-decagon shown below: (a) How many lines of symmetry does the regular do-decagon have? Draw all of the lines of symmetry in the figure above. (b) Determine the angle of rotational symmetry for the regular do-decagon. The Correct Answer and Explanation is: Let&#8217;s break down your questions step by step: (a) Number [&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-245867","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245867","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=245867"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245867\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=245867"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=245867"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=245867"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}