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

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

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

Step-by-step 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

solve for x

step 2

Find the measure of an exterior angle

2x

substitute the value of x

step 3

Find the measure of an interior angle

4x

substitute the value of x

In this problem the regular polygon is a hexagon

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have