prove that sum of the angles of a triangle is 180 degree .
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If ABC is a triangle then <)ABC + <)BCA + <)CAB = 180 degrees.
Proof
Draw line a through points A and B. Draw line b through point C and parallel to line a.
Since lines a and b are parallel,
<)BAC = <)B'CA
and
<)ABC = <)BCA'
It is obvious that
<)B'CA + <)ACB + <)BCA' = 180 degrees.Thus
<)ABC + <)BCA + <)CAB = 180 degrees.