Angles and polygons are used by many different types of engineers, surveyors etc. Particularly in manufacturing and construction.
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It is used in the formula for finding the sum of the interior angles of a polygon:- (n-2)*180 = sum of interior angles whereas 'n' is the number of sides of the polygon
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.
The term congruent is used in comparing two geometrical figures, it does not fit in this context. The angles of a regular polygon are equal.
-- quadrilateral -- parallelogram
Degrees are used to measure angles, not the lengths of sides.