Question

the hexagon below contains diagonals that form six congruent triangles. which rotation about the center of the hexagon can be used to map △a onto △b? a. 60° clockwise b. 120° clockwise c. 180° clockwise d. 240° clockwise

Explanation:

Step1: Find total central - angle of hexagon

The total central - angle around a point is $360^{\circ}$. A regular hexagon is divided into 6 congruent triangles by its diagonals from the center.

Step2: Calculate central - angle of each triangle

The central - angle of each of the 6 congruent triangles is $\frac{360^{\circ}}{6}=60^{\circ}$.

Step3: Determine rotation from $\triangle A$ to $\triangle B$

To map $\triangle A$ onto $\triangle B$, we need to rotate through 2 of these $60^{\circ}$ angles. So the rotation angle is $2\times60^{\circ}=120^{\circ}$ clockwise.

Answer:

B. $120^{\circ}$ clockwise