Triangles in spherical/elliptical geometry

Question

In Euclidean geometry the sum of internal angles of a triangle is always $180^\circ$. In non-Eudlidean geometries it may be either less than this (in hyperbolic geometry) or more (spherical/elliptical geometry). Specifically in the latter the sum is always in between $180^\circ$ and $540^\circ$. However I wonder what is (in spherical or elliptical geometry) that prevent us from treating as triangle rather its outside than inside and concluding that the sum may be actually greater than $540^\circ$?