{"id":6051,"date":"2022-01-28T17:24:43","date_gmt":"2022-01-28T17:24:43","guid":{"rendered":"https:\/\/oryxlearning.com\/company\/?page_id=6051"},"modified":"2022-03-02T16:53:09","modified_gmt":"2022-03-02T16:53:09","slug":"interior-and-exterior-angles-of-regular-polygons-word-problems","status":"publish","type":"page","link":"https:\/\/oryxlearning.com\/learn\/interior-and-exterior-angles-of-regular-polygons-word-problems\/","title":{"rendered":"Interior and Exterior Angles of Regular Polygons Word Problems"},"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 and Exterior Angles of Regular Polygons Word Problems<\/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>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><br \/>\n[\/vc_column_text][vc_column_text el_class=”headingnew”]Rules[\/vc_column_text][vc_column_text]<strong>To find the sum of all interior angles in a regular polygon:<\/strong><br \/>\nThe sum of the interior angles of a polygon can be found by taking the number of sides (n) and subtracting 2. Then, multiply that number by 180.<\/p>\n<p><strong>Sum of interior angles = (n – 2) \u2219 180\u00b0<\/strong><\/p>\n<p><strong>To find the measure of each interior angle in a regular polygon:<\/strong><br \/>\n1. 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.<br \/>\n<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><strong>To find the measure of each exterior angle in a regular polygon:<\/strong><br \/>\nThe measure of one of the exterior angles of a regular polygon can be found by dividing 360 degrees by the number of angles (n).<\/p>\n<p><img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;Measure\\;of\\;one\\;exterior\\;angle&space;=\\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;\">Bees build honeycombs with hexagonal cells. What is the measure of each interior angle of the cell?<\/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\/1605767106267.svg\" width=\"222\" height=\"190\" \/><\/a>[\/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) \u2219 180\u00b0<\/strong><\/p>\n<p>A hexagon has 6 sides, so:<br \/>\n<strong>(6 – 2) \u2219 180 = 4 \u2219 180 = 720\u00b0<\/strong><\/p>\n<p>Since this is a regular hexagon, all of the angles are equal, so divide the sum of the interior angles by 6.<\/p>\n<p><img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;\\frac{720^{\\circ}}{6}={\\color{Red}&space;120^{\\circ}}\" alt=\"\\fn_phv \\frac{720^{\\circ}}{6}={\\color{Red} 120^{\\circ}}\" align=\"absmiddle\" \/>[\/vc_column_text][vc_column_text el_class=”headingnew”]Practice Interior and Exterior Angles of Regular Polygons Word Problems[\/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;\">To manufacture stop signs, the engineers need to determine the measure of each interior angle of the sign. What is the measure of each interior angle if the sign is 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\/1605884996513.svg\" alt=\"Interior and Exterior Angles of Regular Polygons Word Problems Example - Practice Problem 1\" width=\"188\" height=\"352\" \/><\/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;\">Carl is building a new picnic table for his backyard. The table is in the shape of a regular octagon. What is the measure of each exterior angle of the tabletop? <\/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\/1606113263921.png\" alt=\"Interior and Exterior Angles of Regular Polygons Word Problems Example - Practice Problem 2\" width=\"384\" height=\"234\" \/><\/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;\">Marlin is an avid soccer fan and is sewing his own soccer ball. He needs to calculate the angle measure of the shapes on the soccer ball. What is the measure of each interior angle of the regular pentagons? <\/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\/1515839806353.svg\" alt=\"Interior and Exterior Angles of Regular Polygons Word Problems Example - Practice Problem 3\" width=\"167\" height=\"167\" \/><\/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” 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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 and Exterior Angles of Regular Polygons Word Problems [\/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. An exterior angle of a polygon […]<\/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 and Exterior Angles of Regular Polygons Word Problems | 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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