Yes
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There must be exactly one.
A right trapezoid has at least two right angles.
A rectangle is a parallelogram, and neither a trapezoid nor an isosceles trapezoid could have exactly two opposite right angles.So, a quadrilateral that is not a parallelogram and could have exactly two opposite right angles must be a kite.
A trapezoid may have two right angles.
A trapezoid can have up to two right, 90 degree angles for it still to be classified as a trapezoid.