Question

In Fig. 6.44, the side QR of APQR is produced to
a point S. If the bisectors of Z PQR and
Z PRS meet at point T, then prove that
1
ZQTR = ZQPR.
2.
​

Answer 1

Answer:

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 = ∠QPR