# Prove that the sum of a Δ is 180 deg.SUPER URGENT!!!!! PLEASE!!!!!

1
by Yasmin

2014-09-19T21:52:00+05:30

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See diagram.

Draw ABC as any triangle.

Now, draw a straight line parallel to BC through A.
Now angle DAG = angle BAC - opposite angles at an intersection of two lines.

Angle DAE = angle ABC  as they are angles formed by a line AB intersecting
two parallel lines  - included angle.

Angle GAF = angle EAC - opposite angles at intersection of two lines at A
Angle GAF = angle BAC    as BC and FE are parallel. AC is intersecting both
lines. These are included angles.

Sum of these angles at A =  angles DAG + GAF + EAD = 180 degrees.
At any point the total angle 360° degrees is divided into 180° and 180° by a
straight line.

So sum of angles A+B+C = 180° degrees