Pretty interesting to find out. It is always true that sum of angles is always 180 degree if and only if the triangle is lied on a flat surface(plane). Likewise, however, Hyperbolic & Spherical trigonometry don't show this kind of attribute. Hyperbolic triangle can have sum of angles less than 180 degree, whereas Spherical triangle can have more than 180 degree. These would be another case of triangle whose the plane is not flat.