Can anyone please explain how to form a better idea in understanding sum of measures of angles in a triangle is $180^\circ$ ?
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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:
P.S.: I think these are more intuitive facts in geometry.