{"id":5959,"date":"2022-01-28T17:31:31","date_gmt":"2022-01-28T17:31:31","guid":{"rendered":"https:\/\/oryxlearning.com\/company\/?page_id=5959"},"modified":"2022-02-28T18:55:37","modified_gmt":"2022-02-28T18:55:37","slug":"exterior-angles-in-regular-polygons","status":"publish","type":"page","link":"https:\/\/oryxlearning.com\/learn\/exterior-angles-in-regular-polygons\/","title":{"rendered":"Exterior 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>Exterior 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]An <strong>exterior angle<\/strong> of a polygon is the angle that is formed between any side of the polygon and a line extended from the next side. Every polygon has interior and exterior angles. The exterior is the term opposite to the interior which means outside. Therefore exterior angles can be found outside the polygon. The sum of the exterior angles of any polygon is equal to 360\u00b0. Any flat shape or figure is said to have interior or exterior angles only if it is a closed shape.<\/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>[\/vc_column_text][vc_column_text el_class=”headingnew”]Rules[\/vc_column_text][vc_column_text]The sum of the exterior angles of every polygon is 360 degrees.<\/p>\n<p>The measure of one of the exterior angles of a regular polygon can be found by dividing 360 degrees by the number of angles (<strong>n<\/strong><strong>).<\/strong><\/p>\n<p><img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;Measure\\;&space;of\\;one\\;exterior\\;angle=\\frac{360^{\\circ}}{n}\" alt=\"\\fn_phv Measure\\; of\\;one\\;exterior\\;angle=\\frac{360^{\\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 exterior angle in a regular decagon?<br \/>\n<\/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>[\/vc_column_text][vc_column_text el_class=”headingnew”]Solution[\/vc_column_text][vc_column_text]The sum of the exterior angles of every polygon is 360 degrees.<\/p>\n<p>A decagon has 10 angles, so:<\/p>\n<p><img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;Measure\\;&space;of\\;one\\;exterior\\;angle=\\frac{360^{\\circ}}{n}\" alt=\"\\fn_phv Measure\\; of\\;one\\;exterior\\;angle=\\frac{360^{\\circ}}{n}\" align=\"absmiddle\" \/><\/p>\n<p><img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;=\\frac{360^{\\circ}}{10}={\\color{Red}&space;36^{\\circ}}\" alt=\"\\fn_phv =\\frac{360^{\\circ}}{10}={\\color{Red} 36^{\\circ}}\" align=\"absmiddle\" \/>[\/vc_column_text][vc_column_text el_class=”headingnew”]Practice Exterior 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 exterior angle in a regular triangle?<\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/polygons-and-angles\"><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=\"Exterior Angles in Regular Polygons Practice Problem 1\" width=\"100\" height=\"45\" \/><\/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 exterior angle in a regular pentagon?<\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/polygons-and-angles\"><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=\"Exterior Angles in Regular Polygons Practice Problem 2\" width=\"100\" height=\"45\" \/><\/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 exterior angle in a regular octagon?<\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/polygons-and-angles\"><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=\"Exterior Angles in Regular Polygons Practice Problem 3\" width=\"100\" height=\"45\" \/><\/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] Exterior 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]An exterior angle of a polygon is the angle that is formed between any side of the polygon and a line extended from the next side. […]<\/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>Exterior Angles in Regular Polygons | Oryx Learning<\/title>\n<meta name=\"description\" content=\"An exterior angle of a polygon is the angle that is formed between any side of the polygon and a line extended from the next side. Every polygon has interior and exterior angles. 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