Question

the regular polygon below is to be rotated about its center. what is the minimum angle of rotation that would carry the figure onto itself?

Explanation:

Step1: Recall rotation - symmetry formula

For a regular polygon with \(n\) sides, the minimum angle of rotation \(\theta\) that maps the polygon onto itself is given by \(\theta=\frac{360^{\circ}}{n}\).

Step2: Determine the number of sides

The given polygon is a pentagon, so \(n = 5\).

Step3: Calculate the minimum - rotation angle

Substitute \(n = 5\) into the formula \(\theta=\frac{360^{\circ}}{n}\), we get \(\theta=\frac{360^{\circ}}{5}=72^{\circ}\).

Answer:

\(72^{\circ}\)