Such a quadrangle cannot exist. The right angle must be formed by one of the parallel sides and one of the non-parallel sides. Then the angle formed at the other end of that non-parallel side would also be a right angle (the non-parallel side would be a transversal intercepting the two parallels). But then the quadrangle has two right angles, and not just one.
No its Trapezoid
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most likely that there is no given name it still would be a quadrangle
Draw a parallelagram this has the opposite sides parallel and no right angles
The figure, as described, is impossible. If a quadrangle has 2 pairs of parallel sides then the number of right angles can be 0 or 4, but not 2.
A rhombus
Parallel sides do not intersect. Perpendicular sides intersect at a right angle.