The Exterior Angle Inequality says that the measure of an exterior angle of a triangle is greater than the measure of each of its remote interior angles.[br]This theorem is FALSE in Spherical Geometry.[br]However, if we restrict the lengths of the sides of the triangles to be less than pi/2, then the theorem is true for Spherical Geometry. (u = pi above).[br]The theorem is true in Euclidean and Hyperbolic Geometries without any restriction.