Question

An exterior angle in a polygon with all angles are equal is twice of an interior angle.

(i) Find the measure of each angle in it?

(ii) Find the number of sides?

Answer 1

The exterior angles are equal as all the angles are equal.

Let the interior angle is x, then the exterior angle is 2x.

x + 2x = 3x = 180

∴ x = 60

(i) Interior angles are 60° each and exterior angles are 120° each.

(ii) The polygon has 3 sides. It is a triangle.