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.

Question

3 years ago

10

45°, 108° D. 22.5°, 108°

2 answers:

Len [333] · Answer 1 · 2022-05-30T14:11:05+03:00

Len [333]3 years ago

7 0

The answer should be A

skelet666 [1.2K] · Answer 2 · 2022-05-30T16:19:43+03:00

<h2>Answer:</h2>

Option: A is the correct answer.

A. 45°,135°

<h2>Step-by-step explanation:</h2>

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°