Question

prove that the sum of the angles of a triangle is 180°m​

Answer 1

Given :

A triangle ABC.

To prove :

∠A+∠B+∠C=180

⟹∠1+∠2+∠3=180

Construction :

Through A, draw a line L parallel to BC.

Proof :

Since L ∥ BC. Therefore,

∠2=∠4 ….eq(i)

And, ∠3=∠5...… eq (ii)

adding  eq (i) and(ii)

Therefore, ∠2+∠3=∠4+∠5

∠1+∠2+∠3=∠1+∠4+∠5  [adding∠1bothSide]

∠1+∠2+∠3=180

Thus, the sum of three angles of a triangle is 180