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Question
In the given figure, ABCD is a cyclic quadrilateral. AF is drawn parallel to CB and DA is produced to point E. If ∠ADC = 92°, ∠FAE = 20°; determine ∠BCD. Give reason in support of your answer.
Solution
In cyclic quad. ABCD,
AF || CB and DA is produced to E such that ∠ADC = 92° and ∠FAE = 20°
Now, we need to find the measure of ∠BCD
In cyclic quad. ABCD,
`=>` ∠B + ∠D = 180°
`=>` ∠B + 92° = 180°
`=>` ∠B = 180° – 92°
`=>` ∠B = 88°
Since AF || CB, ∠FAB = ∠B = 88°
But, ∠FAE = 20° ...[Given]
Ext. ∠BAE = ∠BAF + ∠FAE
= 88° + 20°
= 108°
But, Ext. ∠BAE = ∠BCD
∴ ∠BCD = 108°
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