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Different pairs of angles have different names.
They are rhombus and parallelogram.
The angles between the sides that are parallel are congruent.The angles between the sides that are parallel are congruent.The angles between the sides that are parallel are congruent.The angles between the sides that are parallel are congruent.
In two dimensions, lines can be parallel, angles cannot. So no plane shape has parallel angles.
Quadrilateral, rectangle, square