Question

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

Answer 1

In ΔQTR,  

∠ TRS = ∠ TQR + ∠ QTR             Exterior angle theorem in a triangle

∠ QTR = ∠ TRS - ∠ TQR ......(I)

Also in ΔQPR,

∠ SRP = ∠ QPR + ∠ PQR  

2∠ TRS = ∠ QPR + 2∠ TQR       ∠TRS and ∠TQR are the bisectors of ∠SRP and ∠PQR respectively

∠ QPR = 2 ∠ TRS - 2 ∠ TQR

∠ TRS - 2 ∠ TQR = 1/2 ∠ QPR .....(II)

From (I) and (II), we get

∠ QTR = 1/2 ∠ QPR  

Thanks me  

Mark me as brainliest :-)

Rate my answers ;)