Answer :
To Prove: ∠QTR = 1/2 ∠QPR
Given: Bisectors of ∠PQR and ∠PRS meet at point T
Proof:
In ΔQTR,
∠TRS = ∠TQR + ∠QTR (Exterior angle of a triangle equals to the sum of the two opposite interior angles)
∠QTR = ∠TRS - ∠TQR -----------(i)
Similarly in ΔQPR,
∠SRP = ∠QPR + ∠PQR
2∠TRS = ∠QPR + 2∠TQR (∵ ∠TRS and ∠TQR are the bisectors of ∠SRP and ∠PQR respectively.)
∠QPR = 2 ∠TRS - 2 ∠TQR
.............(ii)
From (i) and (ii), we get
Hence, proved
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