Vertex angle

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

In geometry, a vertex angle is the angle associated with a vertex of a polygon. Often a vertex angle of a polygon is referred to simply as an angle of the polygon.

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.

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.

See also

• Complementary angles
• Supplementary angles
• Dihedral angle