ABC is an isosceles triangle with AB = AC. The side BA is produced to D such that AB = AD. If ∠ABC = 30°, then ∠BCD is equal to

Answer: Option B

According to question,

In ΔABC
Exterior angle CAD = ∠ABC + ∠ACB
CAD = 2∠ABC (∵ ∠ABC = ∠ACB)
CAD = 2 × 30°
CAD = 60°
In ΔCAD,
∠ACD = ∠ADC = $$\frac{180-\angle \text{CAD}}{2}$$    = 60°
⇒ ∠BCD = ∠ACD + ∠BCA
⇒ ∠BCD = 60° + 30°
⇒ ∠BCD = 90°