A circle is not a polygon because it does not conform to the definition of a polygon. The definition of a polygon is a closed figure formed by straight lines or straight sides. Although the circle is a closed figure, it is not formed by straight line segments.
Another condition for a figure to be classified as a polygon is that its sides must not cross each other. Some examples of polygons are a square, rectangle, hexagon, triangle and pentagon. Polygons also can be convex, concave irregular or regular figures. While concave polygons have reflex angles, convex polygons do not. Regular polygons have sides that are of equal length and all interior angles have equal measurement. Irregular polygons do not conform to this definition of regular polygons.