Editing Internal and external angles (section)

==Extension to crossed polygons==
The interior angle concept can be extended in a consistent way to [[crossed polygon]]s such as [[star polygon]]s by using the concept of [[directed angles]]. In general, the interior angle sum in degrees of any closed polygon, including crossed (self-intersecting) ones, is then given by {{math|180(''n'' − 2''k'')°}}, where {{mvar|n}} is the number of vertices, and the strictly positive integer {{mvar|k}} is the number of total (360°) revolutions one undergoes by walking around the [[perimeter of the polygon|perimeter]] of the polygon. In other words, the sum of all the exterior angles is {{math|2''πk''}} radians or {{math|360''k''}} degrees. Example: for ordinary [[convex polygon]]s and [[concave polygon]]s, {{math|1=''k'' = 1}}, since the exterior angle sum is 360°, and one undergoes only one full revolution by walking around the perimeter.