Find the number of sides of a regular polygon, if each of its interior angle is 162°.

Solution:

Given: Each interior angle of a polygon is 162°.

We know that the sum of an interior angle and an exterior angle of a polygon is equal to 180°.

As interior angles are 162°, each exterior angle is 180°- 162° = 18°

Sum of all the exterior angles of a polygon is always 360^o and as each exterior angle is 18°

The number of angles/sides of the polygon are 360°/18° = 20

Hence, the number of sides of the given polygon is 20.

Find the number of sides of a regular polygon, if each of its interior angles is 162°.

Summary:

The number of sides of a regular polygon, if each of its interior angles is 162° is 20.