Find the measure of an angle in a regular 15-gon polygon.

Question

Polygon, angles

Answer 1

In any n-sided polygon, the sum of the internal angles is always equal to (n-2)pi radians, where n is the number of sides.

When n = 15, sum of the angles is 13pi radians.

Since the polygon is regular then all 15 internal angles are equal.

Therefore each angle is equal to 13pi/15 rad = 13*180/15 degrees. = 13*12 degrees

Angle size = 156*