Question

Patrik rotated the pentagon about its center. What degree measure could he have rotated the pentagon so that is mapped onto itself? A.108 B.180 C.288 D.540

Answer 1

Answer:

Option C is correct.

288 degree measure could he have rotated the pentagon so that is mapped onto itself

Step-by-step explanation:

Given:  Patrik rotated the pentagon about its center.

A Rotational symmetry of a regular polygon is based on the number of vertices it has.

If the Pentagon figure is rotated $360^{\circ}$ about its center, each vertex lands exactly on the top of where it started.

Since you have 5 vertices, so your starting vertex can land in 5 different starting places and still come up with the same figure.

So if you take $\frac{360}{5} = 72^{\circ}$ rotations to each consecutive vertex.

⇒a rotation of 72 degree, 144 degree, 216 degree, 288 degree and 360 degree will result in the same figure.

Therefore, 288 degree measure could he have rotated the pentagon so that is mapped onto itself.