A parallelogram.
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Equal and parallel
They are equal and parallel.
rectangle
It is not possible for a quadrilateral in Euclidean plane geometry to have no equal angles and still have its opposite sides parallel.It's possible for a quadrilateral to have no equal angles and two of its sides parallel (opposite ones, obviously; adjacent sides can't possibly be parallel). That would be a trapezoid.
A square and a rhombus both have all sides equal and opposite sides parallel.