{"id":6046,"date":"2022-01-28T17:27:36","date_gmt":"2022-01-28T17:27:36","guid":{"rendered":"https:\/\/oryxlearning.com\/company\/?page_id=6046"},"modified":"2022-03-02T16:54:57","modified_gmt":"2022-03-02T16:54:57","slug":"interior-angles-in-regular-polygons","status":"publish","type":"page","link":"https:\/\/oryxlearning.com\/learn\/interior-angles-in-regular-polygons\/","title":{"rendered":"Interior Angles in Regular Polygons"},"content":{"rendered":"[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text]\n<h5>Interior Angles in Regular Polygons<\/h5>\n[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]The angles that lie inside a shape, generally a polygon, are said to be <strong>interior angles<\/strong>.<\/p>\n<p><a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/polygons-and-angles\"><img loading=\"lazy\" class=\"alignnone wp-image-5961 size-medium\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/imageedit_3_9157409031-300x235.png\" alt=\"\" width=\"300\" height=\"235\" srcset=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/imageedit_3_9157409031-300x235.png 300w, https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/imageedit_3_9157409031.png 431w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><br \/>\n[\/vc_column_text][vc_column_text el_class=”headingnew”]Rules[\/vc_column_text][vc_column_text]1. To find the measure of one interior angle in a regular polygon, first find the sum of interior angles of the required polygon using the formula given below.<\/p>\n<p><strong>Sum of interior angles = (n – 2) \u2219 180\u00b0<\/strong><\/p>\n<p>2. Next, divide the sum of interior angles by the total number of angles the regular polygon has.<\/p>\n<p><img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;\\frac{(n-2)\\times&space;180^{\\circ}}{n}\" alt=\"\\fn_phv \\frac{(n-2)\\times 180^{\\circ}}{n}\" align=\"absmiddle\" \/>[\/vc_column_text][vc_column_text el_class=”headingnew”]Example[\/vc_column_text][vc_column_text]<strong><span style=\"color: #16a085;\">What is the measure of each interior angle in a regular decagon?<\/span><\/strong><\/p>\n<p><a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/polygons-and-angles\"><img loading=\"lazy\" class=\"alignnone \" src=\"https:\/\/cdn.oryxlearning.com\/media_assets\/1616049577519.svg\" width=\"245\" height=\"213\" \/><\/a><br \/>\n[\/vc_column_text][vc_column_text el_class=”headingnew”]Solution[\/vc_column_text][vc_column_text]To find the measure of one interior angle in a regular polygon, first find the sum of interior angles of the required polygon using the formula given below.<\/p>\n<p><strong>Sum of interior angles = (n – 2) <strong>\u2219<\/strong> 180\u00b0<\/strong><\/p>\n<p>A decagon has 10 sides, so:<br \/>\n<strong>(10 – 2) <strong>\u2219<\/strong> 180 = 8 <strong>\u2219<\/strong> 180\u00b0 = 1,440\u00b0<\/strong><\/p>\n<p>Since this is a regular decagon, all of the angles are equal, so divide the sum of the interior angles by 10.<\/p>\n<p><img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;\\frac{1,440^{\\circ}}{10}={\\color{Red}&space;144^{\\circ}}\" alt=\"\\fn_phv \\frac{1,440^{\\circ}}{10}={\\color{Red} 144^{\\circ}}\" align=\"absmiddle\" \/>[\/vc_column_text][vc_column_text el_class=”headingnew”]Practice Interior Angles in Regular Polygons[\/vc_column_text][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 9px;\">Practice Problem 1<\/h5>\n<p><strong><span style=\"color: #16a085;\">What is the measure of each interior angle in a regular heptagon, rounded to the nearest tenth?<\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/polygons-and-angles\"><br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-5718 size-full\" style=\"margin-top: 11px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/option-input.png\" alt=\"\" width=\"100\" height=\"45\" \/><\/a><a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/polygons-and-angles\"><img loading=\"lazy\" class=\"alignnone\" style=\"margin-top: 11px;\" src=\"https:\/\/cdn.oryxlearning.com\/media_assets\/1616049387347.svg\" alt=\" Interior Angles in Regular Polygons Example - Practice Problem 1\" width=\"246\" height=\"242\" \/><\/a><\/p>\n[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/polygons-and-angles”][\/vc_column_inner][\/vc_row_inner][vc_empty_space][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 9px;\">Practice Problem 2<\/h5>\n<p><strong><span style=\"color: #16a085;\">What is the measure of each interior angle in a regular octagon?<\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/polygons-and-angles\"><br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-5718 size-full\" style=\"margin-top: 11px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/option-input.png\" alt=\"\" width=\"100\" height=\"45\" \/><\/a><a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/polygons-and-angles\"><img loading=\"lazy\" class=\"alignnone\" style=\"margin-top: 11px;\" src=\"https:\/\/cdn.oryxlearning.com\/media_assets\/1616049455422.svg\" alt=\" Interior Angles in Regular Polygons Example - Practice Problem 2\" width=\"259\" height=\"231\" \/><\/a><\/p>\n[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/polygons-and-angles”][\/vc_column_inner][\/vc_row_inner][vc_empty_space][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 9px;\">Practice Problem 3<\/h5>\n<p><strong><span style=\"color: #16a085;\">What is the measure of each interior angle in a regular tetradecagon, rounded to the nearest tenth?<\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/polygons-and-angles\"><br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-5718 size-full\" style=\"margin-top: 11px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/option-input.png\" alt=\"\" width=\"100\" height=\"45\" \/><\/a><a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/polygons-and-angles\"><img loading=\"lazy\" class=\"alignnone\" style=\"margin-top: 11px;\" src=\"https:\/\/cdn.oryxlearning.com\/media_assets\/1616050547476.svg\" alt=\" Interior Angles in Regular Polygons Example - Practice Problem 3\" width=\"255\" height=\"243\" \/><\/a><\/p>\n[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/polygons-and-angles”][\/vc_column_inner][\/vc_row_inner][vc_empty_space][\/vc_column][vc_column width=”1\/3″ css=”.vc_custom_1633369011398{margin-bottom: 50px !important;}”][vc_row_inner el_class=”stickynotee”][vc_column_inner][vc_single_image image=”2265″ img_size=”full” alignment=”center” css_animation=”fadeIn” css=”.vc_custom_1633509989314{border-radius: 10px !important;}” el_class=”stickypin”][vc_column_text]<strong>Polygon<\/strong> – A closed figure formed by three or more segments called sides.\u200b<\/p>\n<p><strong>Interior angle<\/strong> – An angle of a polygon formed by two of its side and is inside the polygon. \u200b\u200b<\/p>\n<p><strong>Exterior angle<\/strong> – An angle formed by one side and the extension of the adjacent side. It is outside the polygon.[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”boxxborder2″]<span style=\"color: #ed5600;\"><strong>Pre-requisite Skills<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/6th-grade\/Classify-Angles-G6\"><span style=\"color: #ed5600;\">Classify Angles<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/6th-grade\/drawing-angles\"><span style=\"color: #ed5600;\">Drawing Angles<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/6th-grade\/estimating-angles\"><span style=\"color: #ed5600;\">Estimating Angles<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/6th-grade\/angle-relationships\"><span style=\"color: #ed5600;\">Angle Relationships<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/6th-grade\/classify-triangles\"><span style=\"color: #ed5600;\">Classify Triangles<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/angles\"><span style=\"color: #ed5600;\">Angles<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/finding-angle-measures\"><span style=\"color: #ed5600;\">Finding Angle Measures<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/complementary-and-supplementary-angles\"><span style=\"color: #ed5600;\">Complementary and Supplementary Angles<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/angles-in-triangles\"><span style=\"color: #ed5600;\">Angles in Triangles<\/span><\/a>[\/vc_column_text][vc_column_text el_class=”boxxborder2″ css=”.vc_custom_1638268255981{border-top-width: 7px !important;border-right-width: 7px !important;border-bottom-width: 7px !important;border-left-width: 7px !important;background-position: center !important;background-repeat: no-repeat !important;background-size: contain !important;border-left-color: #333399 !important;border-left-style: solid !important;border-right-color: #333399 !important;border-right-style: solid !important;border-top-color: #333399 !important;border-top-style: solid !important;border-bottom-color: #333399 !important;border-bottom-style: solid !important;border-radius: 35px !important;}”]<span style=\"color: #333399;\"><strong>Related Skill<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/geometric-proof\"><span style=\"color: #333399;\">Geometric Proof<\/span><\/a>[\/vc_column_text][vc_row_inner equal_height=”yes” el_class=”btninlinespacing”][vc_column_inner][vc_btn title=”Grade 1″ color=”warning” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F1st-grade%2Fmaths|title:Grade%201%20Math||”][vc_btn title=”Grade 2″ color=”danger” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F2nd-grade%2Fmaths|title:Grade%202%20Math||”][vc_btn title=”Grade 3″ color=”violet” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F3rd-grade%2Fmaths|title:Grade%203%20Math||”][vc_btn title=”Grade 4″ color=”blue” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F4th-grade%2Fmaths|title:Grade%204%20Math||”][vc_btn title=”Grade 5″ color=”green” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F5th-grade%2Fmaths|title:Grade%205%20Math||”][vc_btn title=”Grade 6″ color=”info” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F6th-grade%2Fmaths|title:Grade%206%20Math||”][vc_btn title=”Grade 7″ color=”vista-blue” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F7th-grade%2Fmaths|title:Grade%207%20Math||”][vc_btn title=”Grade 8″ color=”mulled-wine” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F8th-grade%2Fmaths|title:Grade%208%20Math||”][\/vc_column_inner][\/vc_row_inner][vc_row_inner equal_height=”yes” el_class=”btninlinespacing”][vc_column_inner][vc_btn title=”Geometry and Spatial sense” color=”warning” link=”url:https%3A%2F%2Foryxlearning.com%2Ftopics%2Fmaths%2Fgeometry-and-spatial-sense|title:Geometry%20and%20Spatial%20sense||”][vc_btn title=”Graphs” color=”danger” link=”url:https%3A%2F%2Foryxlearning.com%2Ftopics%2Fmaths%2Fgraphs|title:Graphs||”][vc_btn title=”Measurement” color=”violet” link=”url:https%3A%2F%2Foryxlearning.com%2Ftopics%2Fmaths%2Fmeasurement|title:Measurement||”][\/vc_column_inner][\/vc_row_inner][\/vc_column][\/vc_row][\/vc_section]\n","protected":false},"excerpt":{"rendered":"<p>[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text] Interior Angles in Regular Polygons [\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]The angles that lie inside a shape, generally a polygon, are said to be interior angles. [\/vc_column_text][vc_column_text el_class=”headingnew”]Rules[\/vc_column_text][vc_column_text]1. To find the measure of one interior angle […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.0 (Yoast SEO v17.6) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Interior Angles in Regular Polygons | Oryx Learning<\/title>\n<meta name=\"description\" content=\"The angles that lie inside a shape, generally a polygon, are said to be interior angles....\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/oryxlearning.com\/learn\/interior-angles-in-regular-polygons\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Interior Angles in Regular Polygons\" \/>\n<meta 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