Question

If a 12-sided regular polygon rotates about its center, at which angle of rotation will the image of the polygon coincide with the preimage?

Answer 1

Central angle of a regular polygon:
Ф = 360° : n. 
If n=12:  Ф = 360° : 12 = 30°
At the angle of rotation Ф = 30°  the image of the polygon will coincide with the preimage.