The rotations that carry a regular pentagon onto itself correspond to its symmetries, which are specific angles of rotation around its center. These include a rotation of 0° (identity), 72° (one vertex to the position of the next), 144° (two vertices), 216° (three vertices), and 288° (four vertices). Each of these rotations results in the pentagon appearing unchanged, effectively mapping each vertex to a new position while maintaining the overall shape. Since there are five vertices, there are five distinct rotational symmetries for the regular pentagon.
In 3-5 sentences, summarize the rotations that carry a regular pentagon onto itself. (4 points)
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