In 3–5 sentences, summarize the rotations that carry a regular pentagon onto itself

Answer 1

The rotations that carry a regular pentagon onto itself are those that rotate the pentagon about its center by angles that are multiples of ${72}^{\circ }$. Specifically, these rotations include $0^{\circ }$ (the identity), ${72}^{\circ }$, ${144}^{\circ }$, ${216}^{\circ }$, and ${288}^{\circ }$. Each rotation aligns a vertex of the pentagon with the position of the next vertex, thus preserving its overall shape and symmetry. These five rotations represent the symmetries of the pentagon in terms of rotation.