Question

What is the angle of rotation of this regular octagon? What is the measure of an interior angle? A. 45°, 135° B. 22.5°, 135° C. 45°, 108° D. 22.5°, 108°

Answer 1

The answer should be A

Answer 2

Option: A is the correct answer.

A. 45°,135°

Explanation:

We know that for a regular polygon with n sides the measure of each of the exterior angle is given by:

`(360\degree)/(n)`

Also, the measure of each of the interior angles of the regular polygon with n sides is given by:

`((n-2)* 180\degree)/(n)`

Here we have n=8 (octagon)

Hence, the measure of each of the exterior angles is:

`(360)/(8)=45\degree`

and measure of each of the interior angles is given by:

`((8-2)* 180)/(8)=(1080)/(8)=135\degree`

Hence,

Measure of interior angle= 135°

and measure of exterior angle= 45°