Question

Prove that the sum of the angles of triangle is 180.

Answer 1

see the picture for the answer of this question. I have proved that the sum of three angles of triangle is 180 degree

Answer 2

Statement : The sum of the angles of a triangle is 180°.

To prove : sum of the angles of ΔABC is 180°

Construction : Draw a line $lm$ parallel to BC.

Proof :

Since $lm$ || BC, we have ;

∠2 = ∠y ..... (i) . [Alternate interior angles]

Similarly,

∠1 = ∠z ....... (ii) . [Alternate interior angles]

Also, sum of angles at a point a on line $lm$ is 180°.

∴ ∠2 + ∠x + ∠1 = 180°

⇒ ∠y + ∠x + ∠z = 180°

⇒ ∠x + ∠y + ∠z = 180°

⇒ ∠A + ∠B + ∠C = 180°

Therefore,

Sum of all angles of a Δ is 180°