What are the properties of regular polygons?

All the Exterior Angles of a polygon add up to 360°, so: Each exterior angle must be 360°/n. (where n is the number of sides). Press play button to see. external angle of regular octagon. Exterior Angle (of a regular octagon). Example: What is the exterior angle of a regular octagon? read more

The"inside" circle is called an incircle and it just touches each side of the polygon at its midpoint. The radius of the incircle is the apothem of the polygon. (Not all polygons have those properties, but triangles and regular polygons do). read more

A regular polygon has equal length sides with equal angles between each side. Any other polygon is an irregular polygon, which by definition has unequal length sides and unequal angles between sides. Circles and shapes that include curves are not polygons - a polygon, by definition, is made up of straight lines. read more

These properties apply to all regular polygons, whether convex or star. A regular n-sided polygon has rotational symmetry of order n. All vertices of a regular polygon lie on a common circle (the circumscribed circle); i.e., they are concyclic points. That is, a regular polygon is a cyclic polygon. read more