Question

if a 12 sides regular polygon rotates about it’s center at which angle of rotation will the image of the polygon coincide with the preimage

Answer 1

360 / 12 = 30

So, it's 30 degrees.

Incidentally, a 12 sided polygon is called a dodecagon.

Answer 2

it will be 30 degrees

a 12 sided thing is a dodecagon.