Question

Find the angle of rotation about the center of the regular pentagon that maps A to B.

A.) 216 degrees
B.) 144 degrees
C.) 72 degrees

Answer 1

Option C. 72°

Explanation:

Area inscribed in a regular pentagon ABCD can be divided in five triangles.

Every triangle form an equal angle at the center of this polygon.

So every angle at origin ∠BOA =
`(360)/(5)=72`

Now we can see that to rotate this pentagon in a way that A replaces B, angle of rotation will be 72° anticlockwise.

Option C. 72° is the correct option.