Question

Provide two different degrees of rotation less than 75°
but greater than 0°
that will turn a regular dodecagon onto itself.

Answer 1

A regular dodecagon has 12 sides. In order to turn it onto itself, we need to find angles of rotation that, when applied repeatedly, will align each vertex of the dodecagon onto another existing vertex.

Option 1: 30° Rotation
A 30° rotation will align every second vertex of the dodecagon back onto itself. This means that after applying six consecutive 30° rotations, every vertex will return to its original position.

Option 2: 60° Rotation
A 60° rotation will align every third vertex of the dodecagon back onto itself. This means that after applying four consecutive 60° rotations, every vertex will return to its original position.

Both of these degrees of rotation (30° and 60°) are less than 75° and greater than 0° and will turn a regular dodecagon onto itself.