What is a four sided figure with opposite sides equal and parallel and opposite angles equal?

If one set of opposite sides is equal and parallel then both are. The figure is a PARALLELOGRAM and the opposite angles of course must be equal.

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Parallelograms include rectangles (four right angles) and rhomboids (two opposite acute angles and two opposite obtuse angles).

A square is a type of rectangle (all sides equal).

A rhombus is a type of rhomboid (all sides equal).

Although a square could be considered an equiangular rhombus, it is usually considered a separate type of shape.