Interior and Exterior Angles of a Polygon

By Mark Ryan

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°.


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