n 3–5 sentences, summarize the rotations that carry a regular pentagon onto itself.(4 points)

Answer 1

A regular pentagon can be rotated by multiples of 72 degrees around its center to map onto itself, as a full rotation of 360 degrees divided by the five vertices results in 72-degree increments (360°/5 = 72°). Specifically, the valid rotations are 0° (identity), 72°, 144°, 216°, and 288° clockwise (or equivalently, 0°, -72°, -144°, -216°, and -288° counterclockwise). Each of these rotations aligns the vertices of the pentagon with other vertices while preserving its shape and symmetry. These rotations constitute the dihedral group \( D_5 \), which describes the symmetries of the pentagon.