Triangles in different geometries

[GeometryIsHARD]

So it has come to my attention that 'different geometries' have different rules for the interior angles of a triangle... What are these different rules for Euclidean, elliptic and hyperbolic geometry? What I'm really wondering though is what knowing these rules about the interior angles tells us about the extiorior angles. does the interior angle + exterior angle have to equal 180 degree's or something? Thanks for anyone with some insight!

 

[fresh_42]

So it has come to my attention that 'different geometries' have different rules for the interior angles of a triangle... What are these different rules for Euclidean, elliptic and hyperbolic geometry? What I'm really wondering though is what knowing these rules about the interior angles tells us about the extiorior angles. does the interior angle + exterior angle have to equal 180 degree's or something? Thanks for anyone with some insight!

Have you already read the article on Wiki on non-Euclidean geometry?
https://en.wikipedia.org/wiki/Non-Euclidean_geometry