Regular Polygon Angle

Free interactive math game: Regular Polygon Angle — Each interior angle. Part of the Geometric Shapes category on MathKite.

Example problems

Taken from the generator that powers this exercise. A fresh set appears every time the page is opened, and the printable worksheet holds ten of them.

  1. Find the measure of each interior angle of a regular 24-sided polygon (24 sides).
  2. Find the measure of each interior angle of a regular 15-sided polygon (15 sides).
  3. Find the measure of each interior angle of a square (4 sides).
  4. Find the measure of each interior angle of a regular nonagon (9 sides).

About this exercise

The size of one corner angle in a regular polygon.

How to solve it

There is a shortcut around the outside: walking the whole boundary turns you through 360 degrees, so each exterior angle of a regular polygon is 360 over n, and the interior angle is 180 minus that.

Worked example

A regular decagon has exterior angles of 360 : 10 = 36 degrees, so each interior angle is 180 - 36 = 144.

Common mistake

Stopping at 360 over n. That is the outside turn — the interior angle is its supplement.