provide two different degrees of rotation, less than 75° but greater than 0° that will turn a regular dodecagon into itself.
A regular dodecagon will turn onto itself after a ? degrees and ? degrees rotation.
A regular dodecagon will turn onto itself after a 30° and a 60° rotation.
First, a 30° rotation will turn the regular dodecagon onto itself. This is because a 30° rotation is equivalent to rotating the dodecagon by 1/12th of a full rotation. Since the dodecagon has 12 equal sides and angles, each 30° rotation will map each side and angle onto itself, resulting in the same shape.
Next, a 60° rotation will also turn the regular dodecagon onto itself. This is because a 60° rotation is equivalent to rotating the dodecagon by 1/6th of a full rotation. As mentioned earlier, the dodecagon has 12 equal sides and angles, so each 60° rotation will map each side and angle onto itself, resulting in the same shape.