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Can we prove that sum of angles of triangle is greater than 180. -assumptions are allowed. If you have any suggestion please let me know

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    $\begingroup$ I am not sure this is the right place for this question. Anyway: ON A SPHERE just take 2 non-coincident points on the equator and consider one of the poles: the sum of the angles is certainly greater tha 180°. This will never work in a flat space (sum=180) or on a hyperbolic surface (sum <180) $\endgroup$ – mattiav27 Oct 10 '14 at 11:53
  • $\begingroup$ This is not a triangle in the classical sense. The triangle is a planar figure and the angle are taken between the lines joining the vortices, not the curves... $\endgroup$ – Martigan Oct 10 '14 at 12:22
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It may depend on your definition of triangle, but at least in Euclidian geometry the sum of interior angles of a triangle (three points connected by straight lines) is always 180°.

See also Sum of Angles in a Triangle.

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