Exterior ∠PRS = ∠PQR + ∠QPR

[Exterior angle property]

Therefore, 1 2 ∠PRS = 1 2 ∠PQR + 1 2 ∠QPR

⇒ ∠TRS = ∠TQR + 1 2 ∠QPR …(i)

But in ∆QTR,

Exterior ∠TRS = ∠TQR + ∠QTR …(ii)

[Exterior angles property] Therefore, from (i) and (ii)

∠TQR + ∠QTR = ∠TQR + 1 2 ∠QPR

⇒ ∠QTR = 1 2 ∠QPR **Proved.**