Question

The measure of an exterior angle of a regular polygon is 2x and the measure of an interior angle is 4x Find the measure of one interior and exterior angle

Answer 1

Part a) The measure of an exterior angle is 60°

Part b) The measure of an interior angle is 120°

Explanation:

step 1

Find the value of x

we know that

A regular polygon has equal sides and equal interior angles

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

so

`2x+4x=180`

solve for x

`6x=180`

`x=30`

step 2

Find the measure of an exterior angle

2x

substitute the value of x

`2x=2(30)=60\°`

step 3

Find the measure of an interior angle

4x

substitute the value of x

`4x=4(30)=120\°`

In this problem the regular polygon is a hexagon