A trapezoid may have right angles, but they are not required. The definition of a trapezoid only specifies that it must be a quadrilateral, or a closed, four-sided shape, and that it must have only one pair of parallel sides.
Because it contains a set of parallel lines, the angle pairs at each end of the trapezoid must be complementary, or have a sum of 180 degrees. If one is a 90-degree angle, its neighbor must also be a right angle, and that end of the trapezoid may resemble a rectangle. To remain within the definition of a trapezoid, then, the two remaining angles must not have 90 degrees. Thus, a trapezoid may have a pair of right angles, but cannot have more.