# 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?

Sep 16, 2016

(360°)/3 = 120° which is the size of each exterior angle.

#### Explanation:

An equilateral triangle has 3 lines of symmetry, but of more importance in this case, it has rotational symmetry of order 3. This means that in a rotation of 360° the same image appears 3 times.

(360°)/3 = 120° which is the size of each exterior angle.

The triangle rotates through the exterior angle so that the next vertex can be in the same position as the previous one.

IN the same way, a square will rotate through 360/4 = 90°

A pentagon will rotate through 360/5 = 72° for the figure to map onto itself.