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.