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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1Maybe this – David Mitra Jan 31 '12 at 21:41
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if a ray stand on a line then the sum of the adjactent angels so formed is 180degree – Jun 30 '12 at 14:46
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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:
- 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.
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+1 Elementary result, of course, but a very nice explanation indeed – Dilip Sarwate Feb 02 '12 at 01:40