A regular octagon is rotated about its center. Which angle of rotation will carry the figure onto itself?

Question

A) 60

B) 105

C) 225

D) 320

Answer 1

The central angle of a regular octagon is 360/8 = 45 degrees. So every time you rotate 45 degrees, the octagon rotates onto itself. You can also rotate any integral multiple of 45 degress, such as 45*2 = 90 degrees or 45*3 = 135 degrees, etc. One of your choices is an integral multiple of 45 degrees. Can you find it? HINT: Divide each choice by 45. If you get an integer, it's the right answer.