**Q) **In the given figure, tangents PQ and PR are drawn to a circle such that ∠RPQ = 30^{0}. A chord RS is drawn parallel to tangent PQ. Find the ∠RQS.

**Ans: **In △PRQ, PQ and PR are tangents from an external point P to circle.

∴ PR = PQ

Since the angles opposites to equal sides are equal

∴ ∠PRQ = ∠PQR

Now, by Angle sum property, in △PRQ, ∠PRQ + ∠PQR + ∠RPQ = 180^{0}

∵ ∠RPQ = 30^{0}

∴ ∠PRQ + ∠PRQ + 30^{0 }= 180^{0}

∴ 2 ∠PRQ + 30^{0 }= 180^{0}

∴ ∠PRQ = 75^{0}

Therefore, ∠PRQ= ∠PQR = 75^{0}

Since PQ ∥ SR, and RQ cuts these 2 lines:

∴ ∠PQR = ∠SRQ = 75^{0 }(Alternate angles)

Since PQ is tangent at Q and QR is chord at Q.

∴ ∠RSQ = ∠PQR = 75^{0 }(∠RSQ in alternate segment of circle]

Now, In △SRQ,

∵ ∠RSQ + ∠SRQ + ∠SQR = 180^{0 }(Angle sum property of a triangle)

∴ 75^{0 }+ 75^{0 }+ ∠SQR = 180^{0}

∴ ∠SQR = 180^{0 }– 150^{0 }

**∴ ∠SQR = 30 ^{0}**