Question

prove that the sum of all triangle is 180 degree ​

Answer 1

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

To prove: sum of the angles of Δ ABC is 180°

Construction: Draw a line parallel to BC.

Proof :

Since $lm$ || BC, we have ;

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

Similarly,

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

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

∴ ∠2 + ∠x + ∠1 = 180°,

⇒ ∠y + ∠x + ∠z = 180°

⇒ ∠x + ∠y + ∠z = 180°

⇒ ∠A + ∠B + ∠C = 180°

Therefore,

The sum of all angles of a Δ is 180°