Question

the sum of three angles of a triangle are 180°. Prove the statement​

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 1 ll BC. Therefore,

⇒ ∠2 = ∠4 .....( by alternate angle) ---eq(i)

⇒ ∠3 = ∠5.....( by alternate angle) ---eq(ii)

Now,

Adding eq (i) and (ii)

Therefore,

⇒ ∠2 + ∠3 = ∠4 + ∠5

⇒ ∠1 + ∠2 + ∠3 = ∠1 + ∠4 + ∠5 ----[ adding ∠1 both Side ]

we get,

⇒ ∠1 + ∠2 + ∠3 = 180°

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

hence proved

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