The term regular polygon is almost always used to refer to a polygon that has equal interior angles and equal side lengths. In that light, the equiangular polygon and a regular polygon are the same thing.
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Regular polygon is equilateral and equiangular. Irregular polygon is non-equilateral and non-equiangular.
Yes, a regular polygon is always equiangular.
It is a regular polygon
A rectangle, for example.
The Equiangular polygon is a classification of polygon which has equal measures of angles. Unlike the regular polygon, in which the measures of the angles are equal and the measures of the sides are equal. For example, look at quadrilaterals (i.e. polygons with 4 sides and 4 angles). A regular quadrilateral is a square; an equiangular quadrilateral is a rectangle. Not all rectangles are squares (although all squares are rectangles).