Question

1. what is the angle of rotation for the following figure? 72° 90° 60° 120°

Explanation:

Step1: Recall rotation - angle formula

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

Step2: Count the number of identical parts

In the given figure, the figure coincides with itself 5 times in a 360 - degree rotation, so $n = 5$.

Step3: Calculate the angle of rotation

Substitute $n = 5$ into the formula $\theta=\frac{360^{\circ}}{n}$. We get $\theta=\frac{360^{\circ}}{5}=72^{\circ}$.

Answer:

$72^{\circ}$