Question

How can I prove Ques no. 6

Answer 1

Hey!!

given,
bisectors of angle PQR and angle PRS meet at point T

To prove,
angle QTR=1/2 angle QPR

Proof,
angle TRS= angle TQR ( exterior angle of a triangle equals to the sum of two interior angles)
angle QTR= angle TRS - angle TQR...(i)
also,
angle SRP= angle QPR + angle PQR
2 angle TRS = angle QPR + 2 TQR
QPR=2 angle TRS - 2 angle TQR
1/2 angle =angle TRS -angle TQR ...(ii)

Equating (i)and (ii)
angle QTR -angle TQR =1/2angle QPR
hence proved


hope this helps you:)