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The Triangle Angle Sum Theorem states that the sum of the measures of the angles of any triangle is <math>180^o</math>.

The '''Triangle Angle Sum Theorem''' states that for any triangle lying in the Euclidean plane that the sum of the angles is equal to <math>180^o</math> or <math> \pi </math> radians.

 

This is one of the facts that characterizes [[Euclidean geometry]]: it is not, however, true in other geometries. The proof for this theorem is reliant on the parallel postulate, so does not generalize into [[Non-Euclidean geometry|other geometries]]. For example, any triangle constructed on the surface of the earth (known as a spherical triangle) the sum of the angles is always greater than <math> 180^o </math>.