Question

determining angles of rotational symmetry of a regular polygon
the regular nonagon has rotational symmetry of which angle measures? check all that apply.
40°
45°
120°
240°
260°
320°

Explanation:

Step1: Calculate the smallest rotation angle

The formula for the smallest rotation angle of a regular \(n -\)gon is \(\frac{360^{\circ}}{n}\). For a nonagon (\(n = 9\)), \(\frac{360^{\circ}}{9}=40^{\circ}\).

Step2: Find other rotation angles

Other rotation angles are multiples of the smallest rotation angle. So, \(k\times40^{\circ}\), where \(k = 1,2,\cdots,8\).
When \(k = 3\), \(3\times40^{\circ}=120^{\circ}\)
When \(k = 6\), \(6\times40^{\circ}=240^{\circ}\)

Answer:

\(40^{\circ}\), \(120^{\circ}\), \(240^{\circ}\)