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

Answer 1

To find degrees of rotation that will turn a regular dodecagon onto itself, we need to consider the symmetries of the dodecagon. A regular dodecagon has 12 sides, meaning it can be rotated by multiples of \( \frac{360^\circ}{12} = 30^\circ \).

The rotations that will map the dodecagon onto itself are given by the multiples of \( 30^\circ \). The valid rotations that are less than 75 degrees but greater than 0 degrees are:

• \( 30^\circ \) (1 × 30)
• \( 60^\circ \) (2 × 30)

Thus, two degrees of rotation that will turn a regular dodecagon onto itself are 30 degrees and 60 degrees.