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Question

# Two circles intersect at B and E. Quadrilaterals ABEF and BCDE are inscribed in these circles such that ABC and FED are line segments. Also, ∠A=96∘ and ∠F=75∘, the value of x is:

A
96
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B
84
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C
75
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D
105
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Solution

## The correct option is B 84∘Given that, ∠A=96∘ ∠F=75∘ In the quadrilateral ABEF, ∠A+∠BEF=180∘ ( In cyclic quadrilateral, sum of opposite angles are supplementary) ∠BEF=180∘−96∘ ∠BEF=84∘ Now, ∠BEF+∠BED=180∘ ⇒∠BED=180∘−84∘ =96∘ In the quadrilateral BCDE, ∠BED+∠C=180∘ ∵∠BED=96∘ ∠C+96∘=180∘ ∠C=180∘−96∘ ⇒∠C=84∘ ⇒x=84∘ So, x=84∘

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