Question

16. Prove that the sum of all three angles of a triangle is 180"
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Answer 1

Answer:

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 .