You could be either a square, a kite, a trapezoid, or a rectangle.
They all consist of at least one right angle and are quadrangles because they have 4 sides (or 4 angles, whichever way you look at it). And the other three angles don't have to be exact, as well as the side lengths. So that's why a kite qualifies as a candidate to this question.
You also may think that Trapezoids can never have right angles, because you always see them like this:
