A regular nonagon is a polygon with nine equal sides and nine equal angles. Rotational symmetry refers to the property of a shape that allows it to be rotated around a center point and still look the same at certain angles. For a regular nonagon, the rotational symmetry is determined by the number of sides it has.
To calculate the angles of rotational symmetry for a regular nonagon, we can use the following formula:
- Rotational Symmetry Angle: 360 degrees divided by the number of sides.
- For a nonagon: 360 degrees / 9 sides = 40 degrees.
This means that a regular nonagon has rotational symmetry at the following angle measures:
- 40 degrees
- 80 degrees
- 120 degrees
- 160 degrees
- 200 degrees
- 240 degrees
- 280 degrees
- 320 degrees
- 360 degrees (or 0 degrees)
In conclusion, the regular nonagon exhibits rotational symmetry at angle measures of 40 degrees, 80 degrees, 120 degrees, 160 degrees, 200 degrees, 240 degrees, 280 degrees, 320 degrees, and 360 degrees. Each of these angles reflects a rotation that returns the nonagon to a configuration indistinguishable from its original position.