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.