Question

select all of the angles of rotation that produce symmetry for this hexagon. a. 30 b. 45 c. 60 d. 90 e. 120 f. 180 3 pts

Explanation:

Step1: Recall rotation - symmetry property of a regular hexagon

A regular hexagon has an order of rotational symmetry of 6. The central angle of a regular hexagon is $\frac{360^{\circ}}{n}$, where $n = 6$ (number of sides). So the central - angle is $60^{\circ}$.

Step2: Identify the angles of rotation for symmetry

The angles of rotation that produce symmetry for a regular hexagon are multiples of the central angle. The possible angles of rotation $\theta$ are given by $\theta=\frac{360^{\circ}}{k}$, where $k$ is a positive integer such that the hexagon maps onto itself. The angles are $60^{\circ},120^{\circ},180^{\circ},240^{\circ},300^{\circ},360^{\circ}$. Among the given options, the angles that produce symmetry for the hexagon are $60^{\circ},120^{\circ},180^{\circ}$.

Answer:

C. 60, E. 120, F. 180