Internal and external angle

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Internal and External angles

In geometry, an interior angle (or internal angle) is an angle formed by two sides of a polygon that share an endpoint. For a simple, convex or concave of the polygon, this angle will be an angle on the inner side of the polygon. A polygon has exactly one internal angle per vertex.

If every internal angle of a simple, closed polygon is less than 180°, the polygon is called convex.

In contrast, an exterior angle (or external angle) is an angle formed by one side of a simple, closed polygon and a line extended from an adjacent side.

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 k = 0, 1, 2, 3 ... represents the number of total revolutions of 360° one undergoes walking around the perimeter of the polygon. In other words, 360k° represents the sum of all the exterior angles. For example, for ordinary convex and concave polygons k = 1, since the exterior angle sum = 360° and one undergoes only one full revolution walking around the perimeter.


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