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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    $\begingroup$ Maybe this $\endgroup$ – David Mitra Jan 31 '12 at 21:41
  • $\begingroup$ if a ray stand on a line then the sum of the adjactent angels so formed is 180degree $\endgroup$ – user34792 Jun 30 '12 at 14:46

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.


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

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  • $\begingroup$ +1 Elementary result, of course, but a very nice explanation indeed $\endgroup$ – Dilip Sarwate Feb 2 '12 at 1:40

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