Question

The exterior angle of a regular polygon is 20 degrees.

A. What is the measure of an interior angle of this polygon?

B. How many sides does this polygon have?

Answer 1

A 160° , B 18 sides

Explanation:

A

the exterior angle + interior angle = 180° , then

interior angle + 20° = 180° ( subtract 20° from both sides )

interior angle = 160°

B

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

since the polygon are regular then the exterior angles are congruent , so

number of sides = 360° ÷ 20° = 18