A square is always equiangular. This means that all the angles are equal and that is the case with any type of square.
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A rectangle is not always equilateral, although it is always equiangular. A rhombus is not always equiangular, but is always equilateral. A square is both equilateral and equiangular.
A rhombus is NEVER equiangular. If it were equiangular it would no longer be a rhombus but a square.
Yes, a regular polygon is always equiangular.
An irregular polygon
square or rhombus