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

Question

A regular dodecagon will turn onto itself after a (answer here) and (answer here) rotation.

Answer 1

A regular dodecagon has 12 sides, and it will turn onto itself with rotations that are multiples of \( \frac{360°}{12} = 30° \).

To find two different degrees of rotation less than 75° but greater than 0°, we can consider the following multiples of 30°:

1. \( 30° \) (which is \( 1 \times 30° \))
2. \( 60° \) (which is \( 2 \times 30° \))

Thus, a regular dodecagon will turn onto itself after a \( 30° \) and \( 60° \) rotation.