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.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 119°.
Given that
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°
∠CDA = 180° - ∠CBA = 180° - 85° = 95°
Now, ∠CDA = ∠DAE = 95°
∠DAF = ∠DAE + ∠EAF = 95° + 24° = 119°
So, ∠BAD = 180 - ∠DAF = 180° - 119° = 61°
Hence, ∠BCD = 180° - 61° = 119°