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Quadrangle isn't a polygon. Quadrilaterals are polygons. One's with possibilities of no right angles include:

Kite

Parallelogram

Rhombus

Complex Quadrilateral

Simple Quadrilateral

Concave Quadrilateral

Convex Quadrilateral

Tangential Quadrilateral

Cyclic Quadrilateral

Bicentric Quadrilateral

Trapezium

Isosceles Trapezium

3-Sided-Equal Trapezium

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Q: What polygon does not have right angles but is a quadrangle?
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