Question

A nonagon with a point at the center.
The regular nonagon has rotational symmetry of which angle measures? Check all that apply.

40°
45°
120°
240°
260°
320°

Answer 1

A regular nonagon has rotational symmetry by any multiple of 360°/9 = 40°. So the valid angles from the list are:

- 40° (1·40°) — yes
- 120° (3·40°) — yes
- 240° (6·40°) — yes
- 320° (8·40°) — yes

45° and 260° are not multiples of 40°, so they are not symmetries.