1. Theorem 1: the exterior angle inequality theorem, is true in Euclidean and hyperbolic space but not true in spherical geometry.

a. Using the Euclidean angle sum theorem, prove theorem 1

b. Using the hyperbolic angle sum theorem, prove theorem 1.

c. Describe a spherical triangle in spherical geometry that is a counterexample to theorem 1. Explain how the spherical triangle proves theorem 1 is false in spherical geometry.