In Fig. 6.44, the side QR of PQR is produced to a point S. If the bisectors of `/_P Q R"\ "a n d/_P R S` meet at point T, then prove that `/_Q T R=1/2/_Q P R`
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Explanation

`angle5=(1)/(2)angle6 " "` ( `:.` RT is the bisector of `anglePRS`)

`=(1)/(2)(angle+angle4)` ( `:.` exterior angle is equal to the sum of opposite interior angels)......(1)
Also, `angle5=angle1+angle3 ` ( exterior angle is equal to the sum of opposite interior angels)......(2)
From (1) and (2), we get
`angle1+(1)/(2)angle4=(1)/(2) (angle2+angle4) " "` (each is equal to `angle5`)
`rArr angle1+(1)/(2)angle4=(1)/(2)angle2+(1)/(2)angle4`
`rArrangle1=(1)/(2)angle2`