in 3-5 sentences, summarize the rotations that carry a regular pentagon onto itself.

Answer 1

There are five distinct rotations that carry a regular pentagon onto itself. The first is a 72-degree rotation, which brings the first vertex to the second, the second to the third, and so on. The second rotation is 144 degrees and moves the first vertex to the third, the second to the fourth, and so on. The third rotation is 216 degrees and brings the first vertex to the fourth, the second to the fifth, and so on. The fourth rotation is 288 degrees and moves the first vertex to the fifth, the second to the first, and so on. Finally, there is a full 360-degree rotation that simply brings the pentagon back to its original position.