Sum of angles of a triangle to zero. For a spherical triangle, the sum of the angles is greater than 180° and can be up to 540°. Specifically, the sum of the angles is where "f" is the fraction of the sphere's area which is enclosed by the triangle. Note that spherical geometry does not satisfy several of Euclid's axioms (including the parallel postulate.) Angles between adjacent sides of a triangle are referred to as "interior" angles in Euclidean and other geometries. "Exterior" angles can be also defined, and the Euclidean triangle postulate can be formulated as the exterior angle theorem. One can also consider the
Special right triangle allows one to quickly calculate various lengths in geometric problems without resorting to more advanced methods. "Angle-based" special right triangles are specified by the relationships of the angles of which the triangle is composed. The angles of these triangles are such that the larger (right) angle, which is 90 degrees or radians, is equal to the sum of the other two angles. The side lengths are generally deduced from the basis of the unit circle or other geometric methods. This approach may be used to rapidly reproduce the values of trigonometric functions for the angles 30°, 45°, and 60°. Special