Yes and all 4 interior angles add up to 360 degrees.
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No. A parallelogram has two pairs of opposite angles that are equal but to be equiangular, all four angles must be the same. That is not necessarily the case in a parallelogram.
No, like a rhombus 2 of the angles are the same (opposite each other) and the other 2 angles are the same (opposite each other).
It is a rhombus or a parallelogram.
If both pairs of opposite sides are the same length, and both pairs of opposite angles are the same, the quadrilateral is a parallelogram (rhombus, rectangle, or square).