I was thinking about how a triangle could have all reflex angles. it would look like a regular triangle but the inside would be the outside and the outside would be the inside.
Such a triangle would have three sides. The outside would extend infinitely without end so it can't be considered a side. Also the triangle would have three angles that are reflex. This would break some theorems about triangles. My question is, could this be a triangle? I looked it up and found no good answer but some places said a triangle cannot have any reflex angles.
This is a fun question! There are a couple of ways you could answer it. If the triangle lives on the surface of a sphere, then 'inside' and 'outside' don't have the same meaning as they used to. There are other surfaces like that, too, like the projective plane.
You're right that some triangle theorems break in these settings; for triangles on the sphere, the angles don't have to sum to 180$^\circ$, for instance.