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      Question

      PQRS is a cyclic quadrilateral. If ∠ P is three times

      of ∠ R and ∠ S is five times of ∠ Q, then the sum of ∠ Q + ∠ R will be:
      A 69° Correct Answer Incorrect Answer
      B 71° Correct Answer Incorrect Answer
      C 77° Correct Answer Incorrect Answer
      D 75° Correct Answer Incorrect Answer

      Solution

      ATQ, As we know ⇒ ∠P + ∠R = 180° [∵ ∠P : ∠R = 3 : 1] ⇒ 4 ∠R = 180° ⇒ ∠R = 45° Similarly, ⇒ ∠S + ∠Q = 180° [∵ ∠S : ∠Q = 5 : 1] ⇒ 6∠Q = 180° ⇒ ∠Q = 30° ⇒ ∠R + ∠Q = 45° + 30° = 75° 

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