Q: What shape has 3 sides and one is a right angle?

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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.

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a right angle triangle.

A right angle triangle

A right triangle has three sides and one right angle.

a right triangle

A polygon with 4 or more sides can have more than one right angle.

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.

Draw a right angle corner, then add 4 more sides that are NOT right angles...

What about the other angle(s). You need at least 3 sides and 3 angles to make a closed figure.

Draw a square / rectangle, a quadrangle is just a shape with 4 sides, as long as one is a right angle your golden

Not here. It would resemble a chevron.