# SOLUTION: What is the sum of the interior angles in a polygon? What is the sum of the exterior angles of a polygon? How do you find the measure of one angle of a polygon?

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 Geometry: Polygons Solvers Lessons Answers archive Quiz In Depth

 Question 398123: What is the sum of the interior angles in a polygon? What is the sum of the exterior angles of a polygon? How do you find the measure of one angle of a polygon?Found 2 solutions by Earlsdon, richard1234:Answer by Earlsdon(6287)   (Show Source): You can put this solution on YOUR website!The sum of the interior angles of a polygon with n sides is given by: degrees. The sum of the exterior angles of a "regular" polygon with n sides is given by: ...and if you simplify this, you get... degrees. The measure of one interior angle of a "regular" polygon with n sides is: Answer by richard1234(5390)   (Show Source): You can put this solution on YOUR website!The sum of the interior angles is since you can draw n-2 non-overlapping triangles within the polygon. The sum of all the interior and exterior angles is simply . If we subtract the total sum of the interior angles, we get , or 360 degrees. Not enough information for the third one, but the average measure is also the measure of an angle of a regular n-gon, or .