A regular nonagon, which is a nine-sided polygon, exhibits rotational symmetry. This means that when rotated around its center, it can match its original shape at certain angles.
To determine the angles at which a regular nonagon has rotational symmetry, we can use the formula for the angle of rotation in regular polygons:
Angle of rotation = 360° / n,
where n is the number of sides. For a nonagon, n = 9.
Using the formula, we get:
Angle of rotation = 360° / 9 = 40°.
This means that a regular nonagon can be rotated by 40°, 80°, 120°, 160°, 200°, 240°, 280°, 320°, and 360° (which brings it back to the starting position) to match its original shape. Therefore, the angles that apply are:
- 40°
- 80°
- 120°
- 160°
- 200°
- 240°
- 280°
- 320°
- 360°
These angles represent the various positions at which the nonagon looks the same after rotation. Thus, all of these angles are correct answers when considering the rotational symmetry of a regular nonagon.