No.
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NO. A trapezoid cannot be a rectangle. If a parallelogram has one right angle then it is a rectangle. A trapezoid doesn't satisfy this condition because a trapezoid is a quadrilateral with exactly one parallel side which means that it doesn't have a right angle.
No parallelogram can have only one right angle. The consecutive angles of a parallelogram must be supplementary, meaning they must add up to 180. 180-90=90, so all the angles must be right angles.
One pair of opposite angle is greater than a right angle.