Question

Each exterior angle of a regular polygon is 24 degrees. Find the number of sides and the measure of each interior angle.

Solution

1. The exterior angles of any polygon add up to 360 degrees.
2. Number of sides = 360 / 24 = 15.
3. Each interior angle = 180 - 24 = 156 degrees.
4. Check: the sum of interior angles is (15 - 2) x 180 = 2,340, and 15 x 156 = 2,340.