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If the sum is not 180° you are not in Euclidean space.

If the three angles of a triangle add up to more than 180° then you are in a spherical geometry, if the sum is less than 180° it is a hyperbolic space.

It must add up to 180 degrees. If not, then it either isn't a triangle, or it is a triangle on some non-planar surface (e.g. a triangle formed by taking three points on a globe).

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Q: What if the angles of a triangle don't add up to 180 degrees?
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