Question:
In the given figure, ABCD is a cyclic quadrilateral in which AE is drawn parallel to CD, and BA is produced. If ∠ABC = 92° and ∠FAE = 20°, find ∠BCD.
Solution:
Given: ABCD is a cyclic quadrilateral.
Then ∠ABC + ∠ADC = 180°
⇒ 92° + ∠ADC = 180°
⇒ ∠ADC = (180° – 92°) = 88°
Again, AE parallel to CD.
Thus, ∠EAD = ∠ADC = 88° (Alternate angles)
We know that the exterior angle of a cyclic quadrilateral is equal to the interior opposite angle.
∴ ∠BCD = ∠DAF
⇒ ∠BCD = ∠EAD + ∠EAF
= 88° + 20° = 108°
Hence, ∠BCD = 108°
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