In the given figure, ABCD is a cyclic quadrilateral in which AE is drawn parallel to CD,

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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