Internal and external angles

Right Interior Exterior Adjacent Vertical Complementary Supplementary Dihedral In geometry, an angle of a polygon is formed by two adjacent sides.

261–264 The interior angle concept can be extended in a consistent way to crossed polygons such as star polygons 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 180(n–2k)°, where n is the number of vertices, and the strictly positive integer k is the number of total (360°) revolutions one undergoes by walking around the perimeter of the polygon.

In other words, the sum of all the exterior angles is 2πk radians or 360k degrees.

Example: for ordinary convex polygons and concave polygons, k = 1, since the exterior angle sum is 360°, and one undergoes only one full revolution by walking around the perimeter.