A quadrangle with one right angle has no special name. It is called a quadrangle or a quadrilateral. Any four-sided shape is a quadrilateral, according to Math Is Fun.
The types of quadrangles that have special names are rectangles, parallelograms, rhombuses, squares, trapezoids and kites. Quadrangles must have interior angles that total 360 degrees. A rectangle has four right angles, and each angle is 90 degrees. A parallelogram does not necessarily have right angles, but opposite angles need to be equal, similar to the rhombus. An isosceles trapezoid has equal angles that come from parallel sides. A kite has equal angles where the two pairs of sides intersect.