In the given figure tangents PQ and PR are drawn from an external point P to a circle with centre O, such that `/_RPO = 30^@`. A chord RS is drawn parallel to the tangent PQ. Find `/_RQS`.

Explanation

We know that the tangetns between two tangents from an external point is supplementary to the angle subtended by the radii at the points of contact.
`:. /_RPQ+/_ROQ=180^(@)`
`implies/_RQO=180^(@)-/_RPQ=180^(@)-30^(@)=150^(@)`
Now, `/_RSQ=(1)/(2)/_ROQ=(1)/(2)xx150^(@)=75^(@)` [`:'` the angle subtended by an arc at the centre is twice the angle subtended on the remaining part of the circle].
`:. /_SQM=/_RSQ=75^(@)` [alternate int. since `RS||PQ`]
Also, `/_PQR=/_RSQ=75^(@)`[ angles in alternate segments].
Now,`/_SQM+/_RQS+/_PQR=180^(@)`[ angles on a straight line]
`:./_RQS=180^(@)-(/_SQM+/_PQR)=180^(@)-(75^(@)+75^(@))=30^(@)`