I would have asked this on a math community but I couldn’t find an active one.
In a spherical geometry, great circles are “straight lines”. As such, a triangle can have two or even three right angles to it.
But what if you go the long way around the back of the sphere? Is that still a triangle?
(Edit:) I guess it’s a triangle! Fair enough; I can’t think of what else you would call it. Thanks, everyone.
The answer is obvious. Depending on the curvature of the object the triangles have higher or lower than 180 degrees angle sums. Flat space just happens to have 0 curvature.