A regular pentagon can be rotated about its center by specific angles to map it onto itself. The rotations that achieve this symmetry are by multiples of \(72^\circ\) (i.e., \(72^\circ\), \(144^\circ\), \(216^\circ\), \(288^\circ\), and \(0^\circ\)). Each of these rotations corresponds to turning the pentagon such that each vertex aligns with the position of the next vertex. Therefore, the five rotations create a total of five symmetrical configurations, including the identity rotation of \(0^\circ\).
In 3–5 sentences, summarize the rotations that carry a regular pentagon onto itself
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