Question

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

Explanation:

Step1: Calculate the angle of rotational symmetry

The formula for the angle of rotational symmetry of a regular \(n -\)sided polygon is \(\frac{360^{\circ}}{n}\). For a nonagon (\(n = 9\)), \(\frac{360^{\circ}}{9}=40^{\circ}\).

Step2: Find other valid angles

Rotational symmetry angles are multiples of \(\frac{360^{\circ}}{n}\).

• \(40^{\circ}\times3 = 120^{\circ}\)
• \(40^{\circ}\times6=240^{\circ}\)

Since \(45^{\circ}=\frac{360^{\circ}}{8}\) (not for nonagon), \(260^{\circ}\div40^{\circ}=6.5\) (not an integer multiple), \(320^{\circ}\div40^{\circ} = 8\) (but \(n = 9\) so not valid as per rotational symmetry of nonagon).

Answer:

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