Question

identify the smallest angle of rotation that maps the image to itself. 72°, 45°, 144°, 180°

Explanation:

Step1: Recall rotation - symmetry property of a regular pentagon

For a regular polygon with \(n\) sides, the angle of rotation \(\theta\) that maps the polygon onto itself is given by \(\theta=\frac{360^{\circ}}{k}\), where \(k = 1,2,\cdots,n\). For a pentagon, \(n = 5\). The smallest non - zero value of \(k\) for which we get a non - zero angle of rotation is \(k = 5\).

Step2: Calculate the angle of rotation

Using the formula \(\theta=\frac{360^{\circ}}{n}\), substituting \(n = 5\), we have \(\theta=\frac{360^{\circ}}{5}=72^{\circ}\).

Answer:

\(72^{\circ}\)