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?

Question

James Atkins · Accepted Answer

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

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.

Aurora Ayala · Answer

undefined Alicia can rotate the equilateral triangle about its center by angles that are multiples of 120 degrees, namely 120°, 240°, and 360° (or 0°, which is equivalent to no rotation). These rotations will map the triangle onto itself, maintaining its original shape and orientation.

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?