Prove in the given figure, side QR of a   is produced to a point S.
If the bisector of   and   meet at the point T, then prove

The correct answer is: Hence proved

∠TQR =  ∠PQR (TQ is the angular bisector )
∠TRS = ∠PRS (TR is the angular bisector )
We  know that in a triangle, the exterior angle is always equal to the sum of the interior opposite angles.
In  PQR ; ∠QPR +∠PQR = ∠PRS ∠QPR  = ∠PRS -∠PQR  — Eq1
In  TQR ;  ∠QTR +∠TQR = ∠TRS — Eq2

Substitute ∠TQR =  ∠PQR and  ∠TRS =   ∠ PRS in Eq2

We get ∠QTR +  ∠PQR = ∠PRS

 ∠QTR  = ∠PRS  -   ∠ PQR

 ∠QTR = (∠PRS-∠PQR)
Substitute Eq1 in the above equation

We get ∠QTR = ∠QPR
Hence proved