Question

identify the smallest angle of rotation that maps the image to itself.

Explanation:

Step1: Recall the formula for the angle of rotation of a regular polygon

The formula for the smallest angle of rotation \( \theta\) that maps a regular \(n -\)sided polygon onto itself is \( \theta=\frac{360^{\circ}}{n}\).

Step2: Identify the number of sides of the polygon

The given polygon is a regular pentagon. A pentagon has \(n = 5\) sides.

Step3: Calculate the angle of rotation

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

Answer:

\(72^{\circ}\)