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Q: What is a quadrangle that has equal opposite angles but they are not right angles and the opposite side are parallel and are equal in length?

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Any parallelogram, including rhombus, but not including rectangle or square.

Rhombus!

Such a quadrangle cannot exist. If the quadrangle's angles are equal, they must be 90 degrees.

A shape with opposite sides parallel and of the same length and four right angles is a rectangle.

You are a rectangle! Note that it does not say all of your sides are of equal length.

A Rhombus

Yes. A parallelogram is defined as having opposite sides that are parallel and equal in length, and opposite angles that are equal.

square

A quadrilateral with 4 right angles and opposite sides that are parallel can be either a rectangle if the adjacent sides are of different length or a square if the adjacent sides are of the same length.

This is a parallelogram, opposite sides are of equal length and opposite angles are equal in size.

A rectangle.

rhombus

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