Question

what is the smallest angle of rotational symmetry that maps a regular nonagon onto itself? enter your answer in the box.

Explanation:

Step1: Recall formula for rotational - symmetry angle

The formula for the smallest angle of rotational symmetry of a regular polygon with \(n\) sides is \(\theta=\frac{360^{\circ}}{n}\).

Step2: Identify number of sides of non - agon

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

Step3: Calculate the angle

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

Answer:

\(40^{\circ}\)