Question

please answer the question 6

Answer 1

Given∆PQR in which the side QR is produced to S such that exterior angle TRS is formed also QT and RT are the bisector of angle PRS respectively.
To prove:- angle QTR=1/2angleQPR
Proof:- In∆ PQR, by ext. angle property
angle P+ angle PQR=angle PRS
angle P= 2angleTQR = 2angleTPS (QT and RT are the bisector of angle PRQ and angle PRS)
1/2angle P +angle TQR=angle TRS
1/2angle P= angle TRS-angle TQR ........I)
Now, In ∆TQR by ext. angle property
angle PQR+angle QTR= angle TRS
angle QTR= angle TRS-angle TQR .......ii)
From equations I) and ii) , we get
angle QTR=1/2angleQPR proved✓✓


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