PQRS is a cyclic quadrilateral. If ∠P is thrice ∠R and ∠S is 5 times ∠Q, what is the sum of ∠Q and ∠R?
Show answer & explanation
Correct answer: A
Explanation
Correct answer is option 1 i.e. 75°
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Concept |
Understanding |
Application |
Fair calculation |
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Sum of opposite angles in cyclic quadrilateral = 180 |
∠P = 3 ∠R and ∠S = 5∠Q
∠P + ∠R = ∠Q + ∠S = 180 |
∠P + ∠R = 180 4 ∠R = 180 ∠R = 45
∠Q + ∠S = 180 6 ∠Q = 180 ∠Q = 30 |
180/4 = 45 180/6 = 30 |
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∠R + ∠Q = 75 |
45 + 30 = 75 |