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? select each correct answer. 60° 90° 120° 180° 240°

Explanation:

Step1: Recall rotational symmetry of equilateral triangle

An equilateral triangle has rotational symmetry of order 3. The full - rotation is 360°.

Step2: Calculate the angles of rotation

The angles of rotation that map an equilateral triangle onto itself are given by $\frac{360^{\circ}}{n}\times k$, where $n = 3$ (order of symmetry) and $k = 1,2,3,\cdots$. When $k = 1$, $\frac{360^{\circ}}{3}\times1=120^{\circ}$; when $k = 2$, $\frac{360^{\circ}}{3}\times2 = 240^{\circ}$; when $k=3$, $\frac{360^{\circ}}{3}\times3=360^{\circ}$. Also, negative rotations are equivalent to positive rotations in terms of mapping the shape onto itself.

Answer:

C. 120°, E. 240°