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Question

# Assertion (A) In the given figure, If O is the centre of the circle and AC is the diameter with ∠APB=120∘, then ∠BQC=150∘. Reason (R) In a cyclic quadrilateral, the sum of opposite angles is 180∘. which of the following is true?

A
(A) is true and (R) is the correct explanation of (A)
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B
(A) is false and (R) is the correct explanation of (A)
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C
(A) is true and (R) is false
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D
Both (A) and (R) are false
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Solution

## The correct option is A (A) is true and (R) is the correct explanation of (A)Given, ∠APB=120∘ In cyclic quadrilateral ACBP, ∠APB+∠ACB=180∘⇒120∘+∠ACB=180∘⇒∠ACB=60∘ Also, ∠ABC=90∘ [angle in a semi circle] ∴InΔABC,∠BAC+∠BCA+∠ABC=180∘⇒∠BAC+60∘+90∘=180∘⇒∠BAC=30∘ Again, in cyclic quadrilateral ACQB, ∠CAB+∠CQB=180∘⇒30∘+∠CQB=180∘∴∠CQB=150∘ Reason (R)True

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