On flat 2d paper, a triangle's internal angles add up to 180 degrees. Drawn on the side of a 3d soccer ball, they add up to 270 degrees.
Can they ever add up to 360 degrees (or even more) as the number of dimensions of the thing that the triangle is drawn on increases beyond 3?
Irrespective of the number of sides, in a spherical triangle, we can choose any angle at a vertex. For example when angles situation at one vertex of equilateral spherical triangles:
In an equilateral point triangle (almost flat) with three vanishing sides the sum of three internal angles tends to $3\times 60^{\circ}=180^{\circ}$ in green and,
for the remaining largest spherical triangle (almost sphere) the sum of three internal angles tends to $3\times 300^{\circ}=900^{\circ}$ in yellow.