If you are saying a quadrilateral that only has two right angles I believe it is a trapezoid. A square or other rectangle, all of which have four right angles, also satisfies all the conditions explicitly given.
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trapezoid
A kite and a trapezium can have exactly two right angles.
There is no such shape because the 4 angles in a 4 sided quadrilateral must add up to 360 degrees no more and no less . Therefore 2 obtuse angles and 2 right angles are greater than 360 degrees which doesn't quite measure up for the requirements of a 4 sided quadrilateral.
At the narrowest category it's either a square or a rectangle
An irregular quadrilateral.