<u>Answer:</u>
The correct answer option is C. a 180° rotation about its center.
<u>Step-by-step explanation:</u>
We are to determine whether which of the transformations will always map a parallelogram onto itself.
We know that a parallelogram has a rotational symmetry of 2 so during a rotaion of 360 degrees, a parallelogram maps onto itself twice, which is at 180^{\circ} and 360^{\circ} about its center.
Therefore, the correct answer option is C. a 180° rotation about its center.