Question

consider the figure showing rotational symmetry. identify the angle rotational symmetry. 90° 120° 180° 60° 45°

Explanation:

Step1: Recall rotation - symmetry formula

The formula for the angle of rotational symmetry of a regular polygon (or a symmetric figure) is $\theta=\frac{360^{\circ}}{n}$, where $n$ is the number of times the figure coincides with itself during a full - 360 - degree rotation.

Step2: Count the number of identical parts

By observing the figure, we can see that the figure coincides with itself 8 times during a 360 - degree rotation, so $n = 8$.

Step3: Calculate the angle of rotational symmetry

Substitute $n = 8$ into the formula $\theta=\frac{360^{\circ}}{n}$, we get $\theta=\frac{360^{\circ}}{8}=45^{\circ}$.

Answer:

$45^{\circ}$