For an ideal triangle, a generalization of hyperbolic triangles, this sum is equal to zero. Spherical geometry 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 180° × (1 + 4f ), 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.) Exterior angles 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 sum of all three exterior angles, that equals to 360° in the Euclidean case (as for any convex polygon), is less than 360° in the spherical case, and is greater than 360° in the hyperbolic case. In differential geometry In the differential geometry of surfaces, the question of a triangle's angular defect is understood as a special case of the Gauss-Bonnet theorem where the curvature of a closed curve is not a function, but a measure with the support in exactly three points – vertices of a triangle. See also Euclid's Elements Foundations of geometry Hilbert's axioms Saccheri quadrilateral (considered earlier than Saccheri by Omar Khayyám) Lambert quadrilateral References Geometry Triangle geometry