smc

The definition of an equiangular parallelogram is that all the angles are equal, and that pairs of sides are parallel. It may be a rectangle, because all the angles are equal and it is a parallelogram. It is not necessarily a regular polygon, because if the polygon is a pentagon, it is not a parallelogram. It is not necessarily a rhombus, because all the angles are not necessarily equal. It may be a square, since it is a parallelogram and all the angles are equal. It is not necessarily a trapezoid, because the angles are not necessarily equal. We have that it could be a square or a rectangle. A square is a rectangle, but a rectangle is not necessarily a square. We want the all-encompassing answer so the answer is a rectange $⟹\boxed{\text{rectangle}}$.