A right angled pentagon.
polygon
A four-sided shape with one right angle is a quadrilateral. There is no more specific term, unless it has more than one right angle or has equal sides.
trapezoid
A right-angle triangle.
No because the interior angles of a four sided shape can't exceed 360 degrees.
A trapezoid would fit the given description
A right angle triangle
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a right triangle
An irregular quadrilateral.
A three-sided shape with one pair of perpendicular lines is called a right triangle. In a right triangle, one angle is a right angle (90 degrees), which means that one pair of sides are perpendicular to each other. The other two angles are acute, measuring less than 90 degrees. The Pythagorean theorem can be used to find the lengths of the sides of a right triangle.
Quadrilateral. No other special name. A kite could have 1 right angle - that's possible, but there is no special name for a quadrilateral with only 1 right angle.