The sum of the angles of a triangle is 180-Theorem

The sum of the angles of a triangle is 180º

Given: A triangle △ PQR and ∠1, ∠2, and ∠3 are angles of triangle △ PQR. 

To prove:  ∠1 + ∠2 + ∠3 = 1800

Construction: Draw a line XPY parallel to QR passing through P. 

Proof: XPY ∥ QR and PQ is transversal

∴ ∠2 = ∠4 (Alternate angles) ….(1)

XPY ∥ QR and PR is transversal

∴ ∠3 = ∠5 (Alternate angles) ….(2)

Now, XPY is a line

Therefore,  ∠1 + ∠4 + ∠5 = 1800    …(3)

 From (1) and (2) 

Substituting value of ∠4 and ∠5 in (3), we get

∠1 + ∠2 + ∠3 = 1800

      The sum of the angles of a triangle is 1800

That is,  ∠1 + ∠2 + ∠3 = 1800

Hence proved.

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