Question

The side QR of ∆PQR is produced to a point S. If the bisector of angle PQR and angle PRS meet at point T. Then prove that angle QTR = 1/2 angle QPR.

Answer 1

given: QR is produced to a point S

TP:angle QTR=1/2 of angle QR

and the proof is in the photo that I send you.

Answer 2

Answer:

∠QTR = 1/2 ∠QPR

Step-by-step explanation:

In ΔQTR, ∠TRS is an exterior angle.

=> ∠QTR + ∠TQR = ∠TRS

=> ∠QTR = ∠TRS − ∠TQR (1)

For ΔPQR, ∠PRS is an external angle.

=> ∠QPR + ∠PQR = ∠PRS

=> ∠QPR + 2∠TQR = 2∠TRS

=>  ∠QPR = 2(∠TRS − ∠TQR)

=> ∠QPR = 2∠QTR [From (1)]

=> ∠QTR = 1/2 ∠QPR

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