The regular nonagon has rotational symmetry of which angle measures? check all that apply.

Consider the center of the nonagon. If we join the center to all the vertices, the central angle of 360°, is divided into 9 equal angles, each with a measure of:

360°/9=40°

So to a nonagon rotated 40°, clockwise or counterclockwise, is indistinguishable from the original one. 

similarly if we rotate 80 ° c.wise or c.c.wise 

in general, a nonagon has a rotational symmetry of 40°n,

where n∈{...-3, -2, -1, 0, 1, 2, 3}...

where 40°n, for n negative, means we are rotating clockwise.

any angle which is a multiple of 40°