{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2016-03-26T20:32:44+00:00","modifiedTime":"2021-07-08T17:37:42+00:00","timestamp":"2022-09-14T18:18:23+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Geometry","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33725"},"slug":"geometry","categoryId":33725}],"title":"Interior and Exterior Angles of a Polygon","strippedTitle":"interior and exterior angles of a polygon","slug":"interior-and-exterior-angles-of-a-polygon","canonicalUrl":"","seo":{"metaDescription":"Learn how to find interior and exterior angles of a polygon with this simple guide, complete with angle formulas for polygons.","noIndex":0,"noFollow":0},"content":"Everything you need to know about a polygon doesn’t necessarily fall within its sides. You may need to find exterior angles as well as interior angles when working with <a href=\"https://www.dummies.com/education/math/pre-algebra/common-polygons/\" target=\"_blank\" rel=\"noopener\">polygons</a>:\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/260923.image0.jpg\" alt=\"image0.jpg\" width=\"388\" height=\"400\" />\r\n<ul class=\"level-one\">\r\n \t<li>\r\n<p class=\"first-para\"><strong>Interior angle: </strong>An interior angle of a polygon is an angle inside the polygon at one of its vertices. Angle <em>Q</em> is an interior angle of quadrilateral <em>QUAD</em>.</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\"><strong>Exterior angle: </strong>An exterior angle of a polygon is an angle outside the polygon formed by one of its sides and the extension of an adjacent side.</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/260924.image1.png\" alt=\"image1.png\" width=\"443\" height=\"43\" /></li>\r\n</ul>\r\nInterior and exterior angle formulas:\r\n<ul class=\"level-one\">\r\n \t<li>\r\n<p class=\"first-para\">The <em>sum</em> of the measures of the <em>interior angles</em> of a polygon with <em>n</em> sides is (<em>n</em> – 2)180.</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">The measure of <em>each interior angle</em> of an equiangular <em>n</em>-gon is</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/260925.image2.png\" alt=\"image2.png\" width=\"399\" height=\"41\" /></li>\r\n \t<li>\r\n<p class=\"first-para\">If you count one exterior angle at each vertex, the <em>sum</em> of the measures of the <em>exterior angles</em> of a polygon is always 360°.</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/260926.image3.png\" alt=\"image3.png\" width=\"535\" height=\"49\" /></li>\r\n</ul>\r\nCheck here for <a href=\"https://www.dummies.com/education/math/geometry/1001-geometry-practice-problems-for-dummies-cheat-sheet/\" target=\"_blank\" rel=\"noopener\">more practice</a>.","description":"Everything you need to know about a polygon doesn’t necessarily fall within its sides. You may need to find exterior angles as well as interior angles when working with <a href=\"https://www.dummies.com/education/math/pre-algebra/common-polygons/\" target=\"_blank\" rel=\"noopener\">polygons</a>:\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/260923.image0.jpg\" alt=\"image0.jpg\" width=\"388\" height=\"400\" />\r\n<ul class=\"level-one\">\r\n \t<li>\r\n<p class=\"first-para\"><strong>Interior angle: </strong>An interior angle of a polygon is an angle inside the polygon at one of its vertices. Angle <em>Q</em> is an interior angle of quadrilateral <em>QUAD</em>.</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\"><strong>Exterior angle: </strong>An exterior angle of a polygon is an angle outside the polygon formed by one of its sides and the extension of an adjacent side.</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/260924.image1.png\" alt=\"image1.png\" width=\"443\" height=\"43\" /></li>\r\n</ul>\r\nInterior and exterior angle formulas:\r\n<ul class=\"level-one\">\r\n \t<li>\r\n<p class=\"first-para\">The <em>sum</em> of the measures of the <em>interior angles</em> of a polygon with <em>n</em> sides is (<em>n</em> – 2)180.</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">The measure of <em>each interior angle</em> of an equiangular <em>n</em>-gon is</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/260925.image2.png\" alt=\"image2.png\" width=\"399\" height=\"41\" /></li>\r\n \t<li>\r\n<p class=\"first-para\">If you count one exterior angle at each vertex, the <em>sum</em> of the measures of the <em>exterior angles</em> of a polygon is always 360°.</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/260926.image3.png\" alt=\"image3.png\" width=\"535\" height=\"49\" /></li>\r\n</ul>\r\nCheck here for <a href=\"https://www.dummies.com/education/math/geometry/1001-geometry-practice-problems-for-dummies-cheat-sheet/\" target=\"_blank\" rel=\"noopener\">more practice</a>.","blurb":"","authors":[{"authorId":8957,"name":"Mark Ryan","slug":"mark-ryan","description":" <p><b>Mark Ryan</b> has taught pre-algebra through calculus for more than 25 years. In 1997, he founded The Math Center in Winnetka, Illinois, where he teaches junior high and high school mathematics courses as well as standardized test prep classes. He also does extensive one-on-one tutoring. He is a member of the Authors Guild and the National Council of Teachers of Mathematics. ","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/8957"}}],"primaryCategoryTaxonomy":{"categoryId":33725,"title":"Geometry","slug":"geometry","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33725"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":[{"articleId":175788,"title":"Trig Identities for Pre-Calculus","slug":"trig-identities-for-pre-calculus","categoryList":["academics-the-arts","math","pre-calculus"],"_links":{"self":"/articles/175788"}},{"articleId":147241,"title":"How to Use the Z-Table","slug":"how-to-use-the-z-table","categoryList":["academics-the-arts","math","statistics"],"_links":{"self":"/articles/147241"}},{"articleId":192609,"title":"How to Pray the Rosary: A Comprehensive 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Interior and Exterior Angles of a Polygon

By: Mark Ryan and

Updated: 07-08-2021

From The Book: Geometry For Dummies

Geometry For Dummies

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Everything you need to know about a polygon doesn’t necessarily fall within its sides. You may need to find exterior angles as well as interior angles when working with polygons:

Interior angle: An interior angle of a polygon is an angle inside the polygon at one of its vertices. Angle Q is an interior angle of quadrilateral QUAD.
Exterior angle: An exterior angle of a polygon is an angle outside the polygon formed by one of its sides and the extension of an adjacent side.

Interior and exterior angle formulas:

The sum of the measures of the interior angles of a polygon with n sides is (n – 2)180.
The measure of each interior angle of an equiangular n-gon is
If you count one exterior angle at each vertex, the sum of the measures of the exterior angles of a polygon is always 360°.

Check here for more practice.

About This Article

This article is from the book:

Geometry For Dummies ,

About the book author:

Mark Ryan is the founder and owner of The Math Center in the Chicago area, where he provides tutoring in all math subjects as well as test preparation. Mark is the author of Calculus For Dummies, Calculus Workbook For Dummies, and Geometry Workbook For Dummies.

This article can be found in the category:

Geometry ,

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