text: Q) In the given figure, tangents PQ and PR are drawn to a circle such that ∠RPQ = 300. 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 = 1800
  
  ∵ ∠RPQ = 300
  
  ∴ ∠PRQ + ∠PRQ + 300 = 1800
  
  ∴ 2 ∠PRQ  + 300 = 1800
  
  ∴  ∠PRQ  = 750
  
  Therefore, ∠PRQ= ∠PQR = 750
  
  Since PQ ∥ SR, and RQ cuts these 2 lines:
  
  ∴ ∠PQR = ∠SRQ = 750   (Alternate angles)
  
  Since PQ is tangent at Q and QR is chord at Q.
  
  ∴ ∠RSQ = ∠PQR = 75(∠RSQ in alternate segment of circle]
  
  Now, In △SRQ,
  
  ∵ ∠RSQ + ∠SRQ + ∠SQR = 1800   (Angle sum property of a triangle)
  
  ∴ 75+ 75+ ∠SQR = 1800
  
  ∴  ∠SQR = 1800 – 150
  
  ∴  ∠SQR = 300
  
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