Question

midterm cumulative test
a nonagon is a nine - sided polygon. if a regular nonagon was rotated about its center point, what is the smallest positive angle of rotation that would carry the figure onto itself?
80°
40°
120°
60°

Explanation:

Step1: Recall rotation - symmetry formula

For a regular polygon with \(n\) sides, the smallest angle of rotation \(\theta\) that maps the polygon onto itself is given by \(\theta=\frac{360^{\circ}}{n}\). Here, \(n = 9\) (since it's a non - agon).

Step2: Calculate the angle of rotation

\(\theta=\frac{360^{\circ}}{9}=40^{\circ}\). But we are looking for angles that are multiples of this smallest angle. We check the given options. \(120^{\circ}\) is a multiple of \(40^{\circ}\) (\(120\div40 = 3\)), while \(80^{\circ}\), \(60^{\circ}\) are not multiples of \(40^{\circ}\) in the context of mapping the non - agon onto itself.

Answer:

C. \(120^{\circ}\)