Sum of Angles in a Triangle.

geometry triangles

How about this?

Here, we use the linear pair axioms (version 1, below) and the fact that the alternate interior angles of are equal when a parallel line is intersected by a transveral.

Linear Pair Axioms:

  1. If a ray stands on line, then the sum of two adjacent angles so formed is $180^\circ$.
  2. If the sum of two adjacent angles is $180^\circ$, then the non-common arms of the angles form a line.

angsumtriangle

P.S.: I think these are more intuitive facts in geometry.

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