Question

prove that sum of all angles of a triangle is 180 degree

Answer 1

draw a triangle ABC now make a parallel line to BC
now there will be three angles where is angle A is situated mark them as angle 1 , angle A , and angle 2
now you can see
angle 1 + angle A + angle 2 = 180..... (1)
since angle 1 = angle B they are alternative angles.....(2)
similarly angle 2 = angle C......(3)
comparing eq 1 2 3
you will get angle A + angle B + angle C = 180

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°