Question

Provide two different degrees of rotation less than 75° but greater than 0° that will turn a regular dodecagon onto itself.(1 point)%0D%0AA regular dodecagon will turn onto itself after a °%0D%0A°%0D%0A and °%0D%0A°%0D%0A rotation.

Answer 1

A regular dodecagon has 12 sides, and it can be rotated onto itself by multiples of its angle of symmetry. The full rotation is 360°, and to find the angle of rotation that maps the dodecagon onto itself, we divide 360° by the number of sides (12):

\[
\text{Angle of rotation} = \frac{360°}{12} = 30°
\]

Since you want two different degrees of rotation less than 75° but greater than 0°, we can take multiples of 30°:

1. **First rotation**: \(30°\) (1 full jump)
2. **Second rotation**: \(60°\) (2 full jumps)

Thus, the degrees of rotation that will turn a regular dodecagon onto itself, and are less than 75°, are:

- 30°
- 60°

So the answer is:

A regular dodecagon will turn onto itself after a **30°** and **60°** rotation.