Are adjacent angles in a parallelogram supplementary?
Your are correct in that statement.
In a parallelogram, opposite angles have equal lengths, and so in each parallelogram there are two pairs of equal angles. In a parallelogram, the angles add up to 360˚. Since there are two pairs of angles and one of each pair is on each side, adjacent angles are supplementary (their sum makes 180˚)
The following diagram explains: