In the adjoining figure, QS is the bisector of an angle `angle PQR`, if `angle SQR=35^(@) and angle PRQ=32^(@)`, then find the value of `angle QSR`.

Explanation

Let us join,O, Q and Q, R
Now, `angle QO` is the central angle produced by the are QR and `angleQOR and angle QSR` are two angles in circle produced by the same are QR.
`:. angle QOR=2 angle QOR ........(1) and angle QOR=2 angle QSR.....(2)`
`:.`from (1) and (2) we get, `2angle QPR=2 angle QSR or, angleQPR= angle SQR`.
Now, `angle PQR=2 angle SQR [ :. QS` is the bisector of `angle PQR`]
`=2xx35^(@)=70^(@) and angle PRQ=32^(@)` (Given)
`:. angle QPR=180^(@)=-(angle PQR+ angle PRQ)`
`=180^(@)-(70^(@)+32^(@)) [ :. angle PQR 70^(@) and angle PRQ=32^(@)]`
`=180^(@)-102^(@)=78^(@)`
Hence `angle QSR=78^(@)`