Question

if the measure of an interior angle of a regular polygon is 120 find the number of the sides in the polygon

Answer 1

6 sides

Explanation:

The exterior angle and interior angle sum to 180° , then

exterior angle + 120° = 180° ( subtract 120° from both sides )

exterior angle = 60°

The sum of the exterior angles of a polygon = 360°

To find number of sides n , divide sum by measure of one exterior angle

n = 360° ÷ 60° = 6

Answer 2

6 sides

Explanation:

Interior angle and exterior angle are linear pair.

Let exterior angle = x

x + 120 = 180

x = 180 - 120

x = 60

Number of sides (n) = 360 ÷ measurement of exterior angle

n = 360 ÷ 60

n = 6