Question

Alicia draws an equilateral triangle and then rotates it about its center. Through which angle measures can she rotate the equilateral triangle to map it onto itself?

a. 60°
b. 90°
c. 120°
d. 180°
e. 240°
f. 300°

Answer 1

The answers should be c. 120° and e. 240°

Explanation:

Consider the provided information.

Equilateral triangle has 3 equal sides.

Now we need to rotate the equilateral triangle so that the equilateral triangle to map it onto itself.

For this we need to rotate each of those sides to an adjacent side. (Shown in figure)

This can be happen 3 times as there are 3 sides,

A circle has 360° and
`(1)/(3)* 360^(\circ)=120^(\circ)`.

Thus, a 120° rotation map it onto itself.

Any other angle multiple of 120° will do the same.

Hence, the answers should be c. 120° and e. 240°