In a circle, ABCD is a cyclic quadrilateral in which AE is drawn parallel to CD, and BA is produced to F. If ∠ABC = 85° and ∠FAE = 24°, find the value of ∠BCD.

Correct option is D

Given:
ABCD is a cyclic quadrilateral.
∠ ABC = 85° , ∠ FAE = 24°
Solution:

So,
∠ ABC + ∠ ADC = 180°
=> 85° + ∠ ADC = 180°
=> ∠ ADC = (180° – 85°) = 95°
AE parallel to CD. (given)
Now,
∠ EAD = ∠ ADC = 95 ° (Alternate angles of AE ǁ CD)
We know that the exterior angle of a cyclic quadrilateral is equal to the interior opposite angle.
∴ ∠ BCD = ∠ DAF
=> ∠ BCD = ∠ EAD + ∠ EAF
= 95° + 24° = 119°
therefore, ∠ BCD = 119°