Question

Deshawn draws a regular pentagon and rotates it about its center. Which angle measures can Deshawn rotate the regular pentagon through to map it onto itself? Select each correct answer. 36° 72° 144° 180° 216° 288° A regular pentagon is divided into 5 equal parts. The lengths of all the sides are equal.

Answer 1

Answer:

Option (2).

Step-by-step explanation:

From the figure of a regular pentagon attached,

Central angle formed at the center of a regular pentagon is given by,

Central angle = $\frac{360}{n}$ degrees

Since, m∠COD ≅ m∠EOD ≅ m∠AOE ≅ m∠AOB ≅ m∠BOC

Therefore, by the rotation of a central angle about the center (∠EOD or ∠COD) pentagon will map on to itself.

Measure of the central angle of the given regular pentagon,

m∠COD = $\frac{360}{5}$

              = 72°

Therefore, Option (2) will be the answer.