The famous Sacchari-Legendre theorem states that the sum of all the angles in a triangle is at most 180 degrees. Two answers are needed: First, this theorem applies with the inclusion of all of Euclid's axioms with the exception of which one? Second, when a triangle exists with the sum of its angles less than 180, what geometry is that triangle in?

The Parallel Postulate(5th), Hyperbolic Geometry