You don't need to worry about the angles. It should be clear that "flips" around the side bisectors as well as 180 degree rotation about the center are motions of the rectangle. Since it is NOT a square, flips around the diagonals and 90 degree rotations about the center are NOT motions.

For the rhombus, flips about the diagonalsaremotions and flips about the side bisectors are not.