Question

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

Answer 1

If ∠X≅∠L , ∠P≅∠M , ∠A≅∠K , PA¯¯¯¯¯¯¯¯≅∠MK¯¯¯¯¯¯¯¯¯¯ , AX¯¯¯¯¯¯¯¯≅∠KL¯¯¯¯¯¯¯¯ , and XP¯¯¯¯¯¯¯¯≅∠LM¯¯¯¯¯¯¯¯¯ , which option below shows a correct congruence statement?(1 point) Responses △XPA≅△KLM triangle upper X upper P upper A congruent to triangle upper K upper L upper M △PAX≅△KLM triangle upper P upper A upper X congruent to triangle upper K upper L upper M △XPA≅△MKL triangle upper X upper P upper A congruent to triangle upper M upper K upper L △PAX≅△MKL

Answer 2

The rotations that carry a regular pentagon onto itself are achieved by rotating the pentagon by a multiple of $\frac{2\pi}{5}$ radians around its center. There are five possible rotations in total: a rotation of $\frac{2\pi}{5}$ radians, $\frac{4\pi}{5}$ radians, $\frac{6\pi}{5}$ radians, $\frac{8\pi}{5}$ radians, and a full rotation of $2\pi$ radians. Each of these rotations preserves the shape and orientation of the pentagon.