Of course - a square and a rectangle are both examples of quadrilaterals !
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No quadrilateral with 2 internal right angles can be anything other than a square or rectangle. The shape described in the question does not exist.Improved Answer:-It could be a trapezoid with two right angles, an acute angle and an obtuse angle.
It is a convex quadrilateral, as the remaining angles could be any two angles with a sum of 180 degrees.
a trapezoid
Both a 'kite' shape and a right-angled trapezium can have exactly two right angles
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.