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

Answer:

Option: A is the correct answer.

                  A. 45°,135°

Step-by-step explanation:

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

                          $\dfrac{360\degree}{n}$

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

                $\dfrac{(n-2)\times 180\degree}{n}$

Here we have n=8 (octagon)

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

      $\dfrac{360}{8}=45\degree$

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

$\dfrac{(8-2)\times 180}{8}=\dfrac{1080}{8}=135\degree$

                   Hence,

          Measure of interior angle= 135°

       and measure of exterior angle= 45°