Vertex angle

In geometry, a vertex angle is an angle associated with a vertex of an n-dimensional polytope. Often a vertex angle of a polygon is referred to simply as an angle of the polygon.[1]

A triangle, with interior vertex angles a, b, and c along with exterior angle d

In higher-dimensional polyhedra and polytopes, a vertex angle is an angle formed by two edges of the polyhedron that both belong to a common two-dimensional face of the polyhedron. That is, it is a vertex angle of one of the polygons that form the polyhedron.

Properties

A vertex angle in a polygon is often measured on the interior side of the vertex. For any simple n-gon, the sum of the interior angles is π(n − 2) radians or 180(n − 2) degrees.[2]

Because more than two lines in a polytope can intersect in the same space, the number of vertex angles from any given vertex is not always one. Because of this, it is sometimes necessary to specify not only the vertex, but also the specific line segments that make up the angle.[3]

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See also

References
  1. https://sites.math.washington.edu/~king/coursedir/m444a03/class/10-21-handout-pentagon.html retrieved October 10 2018
  2. Weisstein, Eric W. "Vertex angle". MathWorld.
  3. https://www.chegg.com/homework-help/definitions/pairs-of-angles-63 retrieved October 8 2018


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