The measure of an exterior angle of a regular polygon is 2x, and the measure of an interior angle is 4x. Using the relationship between interior and exterior angles, find the value of x.

The value of x is 30

Solution:

Given that measure of exterior angle of regular polygon is 2x

The measure of interior angle is 4x

To find: value of x

The sum of an interior angle plus an exterior angle must be equal to 180 degrees (supplementary angles)

measure of exterior angle + measure of interior angle = 180

2x + 4x = 180

6x = 180

x = 30

Finding the measure of an exterior angle

measure of exterior angle = 2x = 2 (30) = 60 degrees

Finding the measure of interior angle

measure of interior angle = 4x = 4 (30) = 120 degrees