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In Euclidean Geometry: If it is a triangle with 3 sides yes it does. In Reimannian Geometry: No, they actually add up to more than 180 degrees. Let's use the Earth. Longitudinal Lines intersect the Equator at 90 degree angles, and originate from the North Pole. Pick any two longitudinal lines, extend them from the North Pole to the Equator, and presto! A triangle with more than 180 degrees.

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Q: Do all interior triangles add up to 180 degrees?
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