{"id":1612,"date":"2022-04-21T07:48:00","date_gmt":"2022-04-21T07:48:00","guid":{"rendered":"https:\/\/www.splashlearn.com\/article-test-new\/?page_id=1612"},"modified":"2023-12-13T15:08:38","modified_gmt":"2023-12-13T15:08:38","slug":"nonagon-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/nonagon","title":{"rendered":"What is a Nonagon? Definition, Types, Shape, Examples, Facts, FAQs"},"content":{"rendered":"\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\"><div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-b32fa4d2-6e3e-404e-be6e-b7049421bf95\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/nonagon#0-what-is-a-nonagon>What Is a Nonagon?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/nonagon#2-types-of-nonagon>Types of Nonagon<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/nonagon#5-number-of-diagonals-in-a-nonagon>Number of Diagonals in a Nonagon<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/nonagon#9-solved-examples-on-nonagon>Solved Examples on Nonagon<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/nonagon#10-practice-problems-on-nonagon>Practice Problems on Nonagon<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/nonagon#11-frequently-asked-questions-about-nonagon>Frequently Asked Questions about Nonagon<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<h2 class=\"wp-block-heading\" id=\"0-what-is-a-nonagon\">What Is a Nonagon?<\/h2>\n\n\n\n<p><strong>A nonagon is a nine-sided polygon or a polygon having 9 sides.&nbsp;<\/strong><\/p>\n\n\n\n<p>A nonagon has 9 vertices, 9 sides, and 9 interior angles. In the given image, we have a nonagon ABCDEFGHI.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>There are 9 sides. (AB, BC, CD, DE, EF, FG, GH, HI, and IA)<\/li>\n\n\n\n<li>There are 9 angles. (\u2220ABC, \u2220BCD, \u2220CDE, \u2220DEF, \u2220EFG, \u2220FGH, \u2220GHI, \u2220HIA, and \u2220IAB)<\/li>\n\n\n\n<li>There are 9 vertices. (A, B, C, D, E, F, G, H, and I)<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"369\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/nonagon.png\" alt=\"Nonagon\" class=\"wp-image-36539\" title=\"Nonagon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/nonagon.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/nonagon-300x179.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>A <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/polygon\">polygon<\/a> is a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/2-dimensional\">two-dimensional shape<\/a> that is closed and has a finite number of sides. The sides of a polygon are made of straight line segments. For any polygon, the number of sides equals the number of interior angles.&nbsp;<\/p>\n\n\n\n<p>A polygon is named after the number of sides. For example, a polygon with three sides is called a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/triangle\">triangle<\/a>, a polygon with 4 sides is called a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/quadrilateral\">quadrilateral<\/a>, a polygon with 5 sides is called a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/pentagon\">pentagon<\/a>, etc.&nbsp;<\/p>\n\n\n\n<p>Similarly, a polygon with 9 sides is called a nonagon. Note that the sides of a nonagon may or may not be of equal length. Based on the lengths of sides, we classify nonagons as regular and irregular nonagons. We will learn about them later in the article.&nbsp;<\/p>\n\n\n\n<p>Here are some examples of nonagons!<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"334\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/nonagon-examples.png\" alt=\"Nonagon - examples\" class=\"wp-image-36540\" title=\"Nonagon - examples\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/nonagon-examples.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/nonagon-examples-300x162.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"1-nonagon-definition\">Nonagon: Definition<\/h2>\n\n\n\n<p>In geometry, a polygon having nine sides and nine angles is called a nonagon.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"2-types-of-nonagon\">Types of Nonagon<\/h2>\n\n\n\n<p>There are three possible ways in which we can classify nonagons that are given below:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Regular Nonagons and Irregular Nonagons<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Regular Nonagons<\/strong>: Nonagons in which all the sides and <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/angle\">angles<\/a> are equal are known as regular nonagons.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"621\" height=\"358\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/regular-nonagon.png\" alt=\"Regular nonagon\" class=\"wp-image-36541\" title=\"Regular nonagon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/regular-nonagon.png 621w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/regular-nonagon-300x173.png 300w\" sizes=\"auto, (max-width: 621px) 100vw, 621px\" \/><\/figure>\n\n\n\n<p>The characteristics of a regular nonagon are as follows:<\/p>\n\n\n\n<p>i) All the sides are equal in length and all the angles are equal in measure.<\/p>\n\n\n\n<p>AB = BC = CD = DE = EF= FG = GH = HI = AI<\/p>\n\n\n\n<p>ii) The sum of all interior angles of a nonagon equals 1260\u00b0.&nbsp;<\/p>\n\n\n\n<p>Each interior angle of a regular nonagon = 140\u00b0<\/p>\n\n\n\n<p>\u2220A = \u2220B = \u2220C =\u2220D = \u2220E = \u2220F = \u2220G = \u2220H = \u2220I =140\u00b0\u00a0<\/p>\n\n\n\n<p>iii) The sum of exterior angles of a nonagon = 360\u00b0\u00a0<\/p>\n\n\n\n<p>iv) A regular nonagon can be inscribed inside a circle. It means that the vertices of a regular nonagon can lie on the boundary of the circle.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"621\" height=\"485\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/a-regular-nonagon-inscribed-in-a-circle.png\" alt=\"A regular nonagon inscribed in a circle\" class=\"wp-image-36542\" title=\"A regular nonagon inscribed in a circle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/a-regular-nonagon-inscribed-in-a-circle.png 621w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/a-regular-nonagon-inscribed-in-a-circle-300x234.png 300w\" sizes=\"auto, (max-width: 621px) 100vw, 621px\" \/><\/figure>\n\n\n\n<p><strong>Irregular Nonagons:<\/strong> Nonagons in which sides and angles are not equal are known as irregular nonagons. Examples of an irregular nonagons are given below:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"399\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/irregular-nonagons.png\" alt=\"Irregular nonagons\" class=\"wp-image-36544\" title=\"Irregular nonagons\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/irregular-nonagons.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/irregular-nonagons-300x193.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li><strong>Convex and Concave Nonagons<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Convex Nonagons: <\/strong>Nonagons in which all the interior angles are less than 180 is known as convex Nonagons. In a convex nonagon, all diagonals lie inside it.&nbsp;<\/p>\n\n\n\n<p><strong>Concave Nonagons:<\/strong> Concave nonagons are the nonagons in which at least one interior angle is greater than 180\u00b0. In the concave nonagons, at least one diagonal lies outside it is known as the concave nonagons.\u00a0<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><thead><tr><th class=\"has-text-align-center\" data-align=\"center\"><strong>Convex Nonagon<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Concave Nonagon<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"169\" class=\"wp-image-36545\" style=\"width: 150px;\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/04\/convex-nonagon.png\" alt=\"Convex nonagon\"><\/td><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"115\" class=\"wp-image-36547\" style=\"width: 150px;\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/04\/concave-nonagon.png\" alt=\"Concave nonagon\"><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li><strong>Simple and Complex Nonagons<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Simple Nonagons: <\/strong>Simple Nonagon is a nonagon which does not intersect itself. Its sides do not cross each other.&nbsp;&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"622\" height=\"441\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/simple-nonagons.png\" alt=\"Simple nonagons\" class=\"wp-image-36548\" title=\"Simple nonagons\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/simple-nonagons.png 622w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/simple-nonagons-300x213.png 300w\" sizes=\"auto, (max-width: 622px) 100vw, 622px\" \/><\/figure>\n\n\n\n<p><strong>Complex Nonagons:<\/strong> Complex nonagons are the nonagons that are self-intersecting and there are additional interior spaces. Its sides cross each other.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"628\" height=\"528\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/complex-nonagon.png\" alt=\"Complex nonagon\" class=\"wp-image-36549\" title=\"Complex nonagon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/complex-nonagon.png 628w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/complex-nonagon-300x252.png 300w\" sizes=\"auto, (max-width: 628px) 100vw, 628px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-interior-angles-of-a-regular-nonagon\">Interior Angles of a Regular Nonagon<\/h2>\n\n\n\n<p>Each interior angle of a regular polygon $= \\frac{180 n &#8211; 360}{n}$, where n = the number of sides of the polygon.<\/p>\n\n\n\n<p>For n = 9, interior angle of a regular polygon $= \\frac{(180 \\times 9) &#8211; 360}{9} = 140\u00b0$\u00a0<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-sum-of-interior-angles-of-a-nonagon\">Sum of Interior Angles of a Nonagon<\/h2>\n\n\n\n<p>Sum of interior angles of a polygon $= (n &#8211; 2) \\times 180\u00b0$, where n is the number of sides.<\/p>\n\n\n\n<p>Since the number of sides of a nonagon $= n = 9$, the sum of angles of a nonagon<\/p>\n\n\n\n<p>$= (9 &#8211; 2) \\times 180\u00b0 = 7 \\times 180\u00b0 = 1260\u00b0$<\/p>\n\n\n\n<p>Thus, the sum of all the interior angles of a nonagon $= 1260\u00b0$<\/p>\n\n\n\n<p><strong>Note:<\/strong> To find the sum of interior angles of a polygon, we can also multiply the number of triangles in the polygon by 180\u00b0.&nbsp;<\/p>\n\n\n\n<p>Sum of interior angles of a nonagon $= 7 \\times 180\u00b0 =\u00a01260\u00b0$<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"629\" height=\"421\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/7-triangles-in-a-nonagon.png\" alt=\"7 triangles in a nonagon\" class=\"wp-image-36550\" title=\"7 triangles in a nonagon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/7-triangles-in-a-nonagon.png 629w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/7-triangles-in-a-nonagon-300x201.png 300w\" sizes=\"auto, (max-width: 629px) 100vw, 629px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-number-of-diagonals-in-a-nonagon\">Number of Diagonals in a Nonagon<\/h2>\n\n\n\n<p>A diagonal is a line that connects two non-adjacent vertices of a polygon.&nbsp;<\/p>\n\n\n\n<p>Number of diagonals of a polygon $= \\frac{n(n &#8211; 3)}{2}$ , where n is the number of sides.<\/p>\n\n\n\n<p>For $n = 9$ in a nonagon, we have<\/p>\n\n\n\n<p>Number of diagonals in a nonagon $= \\frac{9 \\times 6}{2} = 27$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-perimeter-of-a-regular-nonagon\">Perimeter of a Regular Nonagon<\/h2>\n\n\n\n<p>The total length of the boundary of a polygon is known as the perimeter of a polygon.&nbsp;<\/p>\n\n\n\n<p>If each side of regular nonagon is \u201ca\u201d units, the perimeter of a regular nonagon $= 9 \\times a = 9a$ units.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-facts-about-nonagon\">Facts about Nonagon<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>The Latin word &#8220;nonus&#8221; means \u201cninth.\u201d<\/li>\n\n\n\n<li>Nonagon is also known as a \u201c9-gon\u201d or a \u201cnine-sided polygon.\u201d<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we learned about nonagons, polygons with 9 sides. We discussed different types of nonagons and important formulas associated with them. Let\u2019s solve a few examples based on these learned concepts.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-solved-examples-on-nonagon\">Solved Examples on Nonagon<\/h2>\n\n\n\n<p><strong>1. <\/strong><strong>Find the perimeter of a regular nonagon if the length of a side is 8 units?<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Number of sides of a nonagon = 9<\/p>\n\n\n\n<p>Length of each side = 8 units<\/p>\n\n\n\n<p>Perimeter $= 9 \\times 8 = 72$ units<\/p>\n\n\n\n<p><strong>2. <\/strong><strong>If the perimeter of a regular polygon is 45 units, what will be the length of the side?<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Number of sides of a regular nonagon = 9 units<\/p>\n\n\n\n<p>Perimeter = 45 units<\/p>\n\n\n\n<p>In regular polygons, all sides are equal in length.<\/p>\n\n\n\n<p>Length of each side = 45 \u00f7 9 = 5 units<\/p>\n\n\n\n<p><strong>3. One of the interior angles of a nonagon is 220\u00b0. Which type of a nonagon is it?<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>One of the interior angles of a nonagon is <strong>220\u00b0.<\/strong><\/p>\n\n\n\n<p>In a concave polygon, at least one interior angle is greater than 180\u00b0.<\/p>\n\n\n\n<p>Since 220\u00b0 is greater than 180\u00b0, it is a concave nonagon.\u00a0<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"10-practice-problems-on-nonagon\">Practice Problems on Nonagon<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">What is a Nonagon? Definition, Types, Shape, Examples, Facts, FAQs<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Each interior angle of a regular nonagon is<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">180\u00b0<\/div><div class=\"spq_answer_block\" data-value=\"1\">110\u00b0<\/div><div class=\"spq_answer_block\" data-value=\"2\">140\u00b0<\/div><div class=\"spq_answer_block\" data-value=\"3\">144\u00b0<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 140\u00b0<br\/>Each interior angle of a regular nonagon is 140\u00b0.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">The sum of interior angles of a nonagon is  ____.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">1260\u00b0<\/div><div class=\"spq_answer_block\" data-value=\"1\">1620\u00b0<\/div><div class=\"spq_answer_block\" data-value=\"2\">1230\u00b0<\/div><div class=\"spq_answer_block\" data-value=\"3\">1240\u00b0<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 1260\u00b0<br\/>The sum of interior angles of a nonagon is 1260\u00b0.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Which of the following is not true about a regular nonagon?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Each central angle measures 140\u00b0.<\/div><div class=\"spq_answer_block\" data-value=\"1\">The sum of all angles of a nonagon $= 1340\u00b0$<\/div><div class=\"spq_answer_block\" data-value=\"2\">All the sides of a regular nonagon are equal.<\/div><div class=\"spq_answer_block\" data-value=\"3\">It has 9 lines of symmetry.<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: The sum of all angles of a nonagon $= 1340\u00b0$<br\/>The sum of all angles of a nonagon $= (9 - 2) \\times 180 = 1260\u00b0$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">How many sides does a Nonagon have?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">5<\/div><div class=\"spq_answer_block\" data-value=\"1\">4<\/div><div class=\"spq_answer_block\" data-value=\"2\">9<\/div><div class=\"spq_answer_block\" data-value=\"3\">6<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 9<br\/>A nonagon has 9 sides.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"What is a Nonagon? 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a nonagon is 1260\u00b0.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following is not true about a regular nonagon?\",\n                    \"text\": \"Which of the following is not true about a regular nonagon?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The sum of all angles of a nonagon $$= (9 - 2) \\\\times 180 = 1260\u00b0$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Each central angle measures 140\u00b0.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The sum of all angles of a nonagon $$= (9 - 2) \\\\times 180 = 1260\u00b0$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"All the sides of a regular nonagon are equal.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The sum of all angles of a nonagon $$= (9 - 2) \\\\times 180 = 1260\u00b0$$\"\n                                    }\n                                }, {\n                                \"@type\": 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1260\u00b0$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The sum of all angles of a nonagon $$= (9 - 2) \\\\times 180 = 1260\u00b0$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"How many sides does a Nonagon have?\",\n                    \"text\": \"How many sides does a Nonagon have?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"A nonagon has 9 sides.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                  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\n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"11-frequently-asked-questions-about-nonagon\">Frequently Asked Questions about Nonagon<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-2a3afd84-1ae3-4c1e-8aa5-bcdecebc39f0\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-2a3afd84-1ae3-4c1e-8aa5-bcdecebc39f0\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-2a3afd84-1ae3-4c1e-8aa5-bcdecebc39f0\"><strong>What is the sum of all exterior angles of a nonagon?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-2a3afd84-1ae3-4c1e-8aa5-bcdecebc39f0\">\n\n<p>The sum of all exterior angles of any polygon is always <strong>360\u00b0. <\/strong>So, the sum of all exterior angles of a nonagon will also be <strong>360\u00b0.<\/strong><\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-2a3afd84-1ae3-4c1e-8aa5-bcdecebc39f0\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-2a3afd84-1ae3-4c1e-8aa5-bcdecebc39f0\"><strong>How do we derive the formula for the number of diagonals of a polygon?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-2a3afd84-1ae3-4c1e-8aa5-bcdecebc39f0\">\n\n<p>Consider a polygon with n vertices and n sides. Diagonal of a polygon is a line-segment joining two non-adjacent vertices. We can choose 2 vertices from n vertices in nC2 ways $= \\frac{n(n &#8211; 1)}{2}$ ways. We have to remove the pairs of adjacent vertices from this selection. There are n such pairs possible.<br>Thus, the number of diagonals $= \\frac{n(n &#8211; 1)}{2} &#8211; n = \\frac{n^{2} &#8211; n &#8211; 2n}{2} = \\frac{n^{2} &#8211; 3n}{2} = \\frac{n(n &#8211; 3)}{2}$<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-2a3afd84-1ae3-4c1e-8aa5-bcdecebc39f0\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-2a3afd84-1ae3-4c1e-8aa5-bcdecebc39f0\"><strong>How many lines of symmetry does a regular nonagon have?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-2a3afd84-1ae3-4c1e-8aa5-bcdecebc39f0\">\n\n<p>There are 9 lines of symmetry in a regular nonagon.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-2a3afd84-1ae3-4c1e-8aa5-bcdecebc39f0\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-2a3afd84-1ae3-4c1e-8aa5-bcdecebc39f0\"><strong>Does a regular nonagon possess rotational symmetry?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-2a3afd84-1ae3-4c1e-8aa5-bcdecebc39f0\">\n\n<p>Yes. A regular nonagon has a rotational symmetry of 40<strong>\u00b0<\/strong>. The order of rotational symmetry is 9.<\/p>\n\n<\/div><\/div>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>What Is a Nonagon? A nonagon is a nine-sided polygon or a polygon having 9 sides.&nbsp; A nonagon has 9 vertices, 9 sides, and 9 interior angles. In the given image, we have a nonagon ABCDEFGHI. A polygon is a two-dimensional shape that is closed and has a finite number of sides. The sides of &#8230; <a title=\"What is a Nonagon? Definition, Types, Shape, Examples, Facts, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/nonagon\" aria-label=\"More on What is a Nonagon? Definition, Types, Shape, Examples, Facts, FAQs\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-1612","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1612","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=1612"}],"version-history":[{"count":11,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1612\/revisions"}],"predecessor-version":[{"id":36554,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1612\/revisions\/36554"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=1612"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=1612"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=1612"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}