An irregular polygon
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Yes, a regular polygon is always equiangular.
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.
A square is always equiangular. This means that all the angles are equal and that is the case with any type of square.
Yes, by definition. If it not equilateral AND equiangular, then it is not regular.