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 pre image

Answer 1

The Central Angle of a regular polygon is 360°÷ the # of sides. So 360°/12 = 30°
This means that a rotation of degree of any multiple of 30 will coincide the image with the original.
So 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, 360.