Question

the side QR of a triangle PQR is produced to a point S. if the bisector of angle PQR and angle PRS meet at point T, QPR (seing in the figure ) then prove that angle QRT=1 /2 angle QPR​

Answer 1

Answer:

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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 (As QT and RT are angle bisectors)

∠QPR = 2(∠TRS − ∠TQR)

∠QPR = 2∠QTR [By using equation (1)]

∠QTR = 1/2 ∠QPR

HENCE PROVED