Question

In a regular polygon, the measure of an interior angle is 6.5 times the measure of an exterior angle. How many sides does the polygon have?

Answer 1

15 sides

Explanation:

Always the sum of interior angle and exterior angle = 180

Let the exterior angle = x

Interior angle = 6.5 *x = 6.5x

x + 6.5x = 180

7.5x = 180

x = 180/7.5

x = 24

Exterior angle = 24°

Sum of exterior angles of any polygon = 360

number of side = Sum of exterior angles ÷ measure of each exterior angle

= 360 ÷ 24

= 15