Question

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

Answer 1

Step-by-step explanation:

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 °