Question

at which angle will the hexagon rotate so that it maps onto itself?
60°
90°
120°
180°

Explanation:

Step1: Recall rotation - symmetry formula

The formula for the angle of rotation $\theta$ of a regular $n$ - sided polygon that maps it onto itself is $\theta=\frac{360^{\circ}}{k}$, where $k$ is a positive integer and for the smallest non - zero rotation, $k$ is the number of sides of the polygon. For a hexagon, $n = 6$.

Step2: Calculate the angle of rotation

Substitute $n = 6$ into the formula $\theta=\frac{360^{\circ}}{n}$. So, $\theta=\frac{360^{\circ}}{6}=60^{\circ}$. Also, multiples of this angle will also map the hexagon onto itself. For example, when $k = 2$, $\theta=\frac{360^{\circ}}{2}=180^{\circ}$, when $k = 3$, $\theta=\frac{360^{\circ}}{3}=120^{\circ}$. The smallest non - zero angle of rotation that maps a regular hexagon onto itself is $60^{\circ}$.

Answer:

A. $60^{\circ}$