A rectangle is a parallelogram, and neither an isosceles trapezoid nor a kite could have exactly two adjacent right angles. So, a quadrilateral that is not a parallelogram and could have exactly two adjacent right angles must be a trapezoid.
You cant have a parallelogram with only 2 right angles If 2 right angles are equal the other 2 must be right angles also. This will be a parallelogram - also it will be either a rectangle or a square.
