a triangle
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a right triangle
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.
It fits the description of a right angle triangle
There is no name for such a figure. Quadrilaterals such as a trapezium or kite or even one with no equal sides can have a right angle.
What about the other angle(s). You need at least 3 sides and 3 angles to make a closed figure.