which of the following rotations will map a regular octagon onto itself

Question

30 counterclockwise

45 counterclockwise

60 counterclockwise

75 counterclockwise

Answer 1

An Octagon has 8 sides. 

 

To rotate the Octagon onto itself, we have to rotate each of those sides to an adjacent side.  That is (1/8)th of a full-circle  turn.

 

A circle has 360° and (1/8)360° = 45°.  A 45° rotation counterclockwise puts each of the edges over the position where an adjacent edge was located.