Question

Prove the sum of three angles of a triangle is 180 degrees .

Answer 1

FROM Δ ABC 
draw a parallel line DE ║ BC
∠DAB + ∠BAC +∠CAE = 180
∠DAB = ∠ABC (ALTERNATE ANGLES ARE EQUAL)
∠CAE = ∠ACB (ALTERNATE ANGLES ARE EQUAL)
SO, ∠ABC + ∠ACB + ∠BAC =180

Answer 2

Knowing that the alternate interior angles are equal lets you substitute the angles of the triangle for the angles of the line. Thus we get, Angle ABC + angle BAC + angle ACB = 180°. In other words, in the triangle ABC, angle B + angle A + angle C = 180°. Thus, the sum of all the angles of a triangle is 180°.