Question

Given : CAT is a triangle, line BD|| AT
Prove that: the sum of the angles of a triangle is 180°.​

Answer 1

Given :

A triangle ABC.

To prove :

∠A+∠B+∠C=180o⟹∠1+∠2+∠3=180o

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=180o

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