The correct answer is e) kite.
A kite is a quadrilateral that has two distinct pairs of adjacent sides that are equal in length. One of the defining properties of a kite is that it has exactly one pair of opposite angles that are congruent. This occurs where the two equal-length sides meet. In contrast, a parallelogram, rectangle, rhombus, and square have two pairs of opposite angles that are congruent. A trapezoid, while it may have one pair of opposite angles that are supplementary, does not necessarily have any angles that are congruent. Therefore, the kite is the shape that satisfies the given condition of having exactly one pair of congruent opposite angles.