Question

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

A regular dodecagon will turn onto itself after a ___ degree and ___ degree rotation.

Answer 1

A regular dodecagon has 12 sides, and it will turn onto itself after any rotation that is a multiple of its internal angle, specifically \( \frac{360^\circ}{12} = 30^\circ \).

To find two different degrees of rotation less than 75 degrees but greater than 0 degrees that will turn a regular dodecagon onto itself, we can use the multiples of \( 30^\circ \).

The valid rotations are:
- \( 30^\circ \) (1 × 30)
- \( 60^\circ \) (2 × 30)

Therefore, a regular dodecagon will turn onto itself after a **30 degree** and **60 degree** rotation.