SOLUTION
A dodecagon has rotational symmetry of order 12 (has 12 sides)

This means that for every rotation of 30 degrees, the dodecagon results in a rotation onto itself. This includes all the degrees that are multiples of 30.
And, 540 degrees, is a multiple of 30, so a rotation of 540 degrees will result in a rotation onto itself.
To know how many times:
