Question

The measure of an exterior angle of a regular polygon is 72°. How can you find the measure of an interior angle of the polygon?

A. add 72 degrees to 90 degrees

B. Subtract 72° from 90°.

C) Subtract 72° from 108°

D) Subtract 72° from 180°.

Answer 1

Option C) Subtract 72° from 180°

Explanation:

We are given the following in the question:

Measure of exterior angle = 72°

Properties of exterior angles:

• An exterior angle of a polygon is an angle at a vertex of the polygon but outside the polygon.
• It is formed by one side and the extension of an adjacent side.
• The interior and exterior angles are supplementary.
• Thus, the sum of the interior angle and the exterior angle is 180 degrees.
• All the exterior angles of a regular polygon are equal in measure.

Thus, we can write:

Let x degrees be the measure of the interior angle. Thus, we can write:

`x + 72 = 180\\x = 180-72 = 108^\circ`

The measure of the interior angle is 108 degrees.

Thus, the correct answer is:

Option C) Subtract 72° from 180°