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Question

ABCD is a cyclic quadrilateral AE is drawn parallel to CD and BA is produced. If ABC=92 and FAE=20, then BCD=
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A
88
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B
108
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C
115
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D
72
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Solution

The correct option is D 108
We know that exterior angle of a cyclic quadrilateral is equal to the interior opposite angle
Also, in a cyclic quadrilateral ABCD, sum of opposite angles is 180

ADC+ABC=180

ADC+92 = 180

ADC=88

EAD=ADC=88 (Alternate interior angles of parallel lines CD and AE)

FAD=20+88=108

BCD=FAD=108 (Exterior angle of a cyclic quadrilateral)

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