Question

what is the smallest degree measure for a regular nonagon to rotate onto itself? (1 point) 40° 60° 30° 80°

Explanation:

Step1: Recall rotation - symmetry formula

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

Step2: Identify \(n\) for non - agon

A non - agon has \(n = 9\) sides.

Step3: Calculate the angle of rotation

Substitute \(n = 9\) into the formula \(\theta=\frac{360^{\circ}}{n}\), we get \(\theta=\frac{360^{\circ}}{9}=40^{\circ}\).

Answer:

A. \(40^{\circ}\)