Question

# Prove that the sum of all angles of a triangle is $180^\circ$ .

In this question we have to use construction and use the properties of parallel lines . Use substitution of angles of the triangle with the angles on the straight line to get to the final answer .

$\angle ABC = \angle EAB$ ( alternate angles are equal as lines BC and EF are parallel )
$\angle BCA = \angle FAC$ ( alternate angles )
Now we know that the sum of all linear angles is $180^\circ$
Therefore $\angle EAB + \angle BAC + \angle FAC = 180^\circ$
$\angle ABC + \angle CAB + \angle ACB = 180^\circ$
Hence proved the sum of all angles of a triangle is $180^\circ$