Can anyone please explain how to form a better idea in understanding sum of measures of angles in a triangle is $180^\circ$ ?
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:
- If a ray stands on line, then the sum of two adjacent angles so formed is $180^\circ$.
- If the sum of two adjacent angles is $180^\circ$, then the non-common arms of the angles form a line.
P.S.: I think these are more intuitive facts in geometry.