Sum of Exterior Angles of a Polygon

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You can move the vertices to create a polygon and add vertices by alt + clicking. When you move the "align" slider all the way to the right, exterior angles of the polygon are aligned on a unique point and forms a full angle, .


Blue colored angles represent counter-clockwise, i.e. positive, angle and orange ones are vice versa. For a positive directed simple polygon, convex positive angles are blue and concave ones are orange. Therefore their algebraic sum is . In general, for any polygon, convex or concave, simple or self-intersecting, this sum is , where is an integer, represents winding number. For example, for a pentagram and for butterfly shaped polygon .


Contributed by: Okay Arik (March 2011)
Open content licensed under CC BY-NC-SA



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