In Figure, the side QR of △PQR is produced to a point S. If the bisectors of ∠PQR and ∠PRS meet at point T, then prove that ∠QTR = 1/2 ∠QPR.

Given, Bisectors of ∠PQR and ∠PRS meet at point T.
To prove: ∠QTR = 1/2 ∠QPR.
Proof,
∠TRS = ∠TQR + ∠QTR (Exterior angle of a triangle equals to the sum of the two interior angles)
⇒ ∠QTR = ∠TRS - ∠TQR (i)
Also ∠SRP = ∠QPR + ∠PQR
2∠TRS = ∠QPR + 2∠TQR
∠QPR = 2∠TRS - 2∠TQR
⇒ 1/2 ∠QPR = ∠TRS - ∠TQR (ii)
Equating (i) and (ii),
∴ ∠QTR = 1/2 ∠QPR [hence proved]