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?
36°
72°
144°
180°
216°
288°

Answer 1

I think the answers are 72, 144, 216, and 288.

Answer 2

Answer:

72°.144° ,216° and 288° .

Step-by-step explanation:

Since we know that a regular pentagon has 5 vertices and has interior angles each measures 72°. In addition a regular pentagon has a rotational symmetry.

If we rotate a regular pentagon by 72° about its center the first vertex will land onto second vertex and so on giving us the same pentagon. Any multiple of 72 will also map the vertexes of pentagon on each other resulting same pentagon.

Now let us look at our options. 144, 216 and 288 are multiples of 72. Therefore, by angle measures 72°.144° ,216° and 288° Deshawn can rotate the regular pentagon through to map it onto itself.