Which rotation will carry a regular octagon onto itself?

Question

A. 60 counterclockwise rotation

B. 90 counterclockwise rotation

C. 120 counterclockwise rotation

D. 200 counterclockwise rotation

Answer 1

A regular octagon has eight sides of equal length and eight equal angles. Thus, it must be unchanged by a rotation of 360°/8 = 45 °, just as a regular triangle, for instance, is unchanged by a 120° degree rotation. Any integer multiple of this must also carry the octagon onto itself. Thus, a 90° rotation, which is twice this, will also work.