Question

complete the following sentence. the figure below has rotational symmetry. is the smallest possible rotation that results in the figure being mapped onto itself.

Explanation:

Step1: Identify symmetry order

The figure has 4 identical repeating segments, so its rotational symmetry order $n=4$.

Step2: Calculate smallest rotation

Use formula for smallest rotational angle: $\frac{360^\circ}{n}$
Substitute $n=4$: $\frac{360^\circ}{4}=90^\circ$

Answer:

The figure below has 4-fold rotational symmetry.
$\boldsymbol{90^\circ}$ is the smallest possible rotation that results in the figure being mapped onto itself.