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The side QR of triangle 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 =Half of angle QPR?
Ref: https://edurev.in/question/508084/The-side-QR-of-triangle-PQR-is-produced-to-a-point-S-If-the-bisector-of-angle-PQR-and-angle-PRS-mee

Angle of triangal - Class 9

In ΔQTR, ∠TRS is an exterior angle.

Angle of triangal - Class 9∠QTR + ∠TQR = ∠TRS
∠QTR = ∠TRS − ∠TQR    (1)

For ΔPQR, ∠PRS is an external angle.

Angle of triangal - Class 9∠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

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