In a ∆ ABC, AB = AC and BA is produced to D such that

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In a ∆ ABC, AB = AC and BA is produced to D such that AC = AD. Then the ∠ BCD is

1. 100°
2. 60°
3. 80°
4. 90°

Correct Option: D

According to question , we draw a figure of a triangle ABC

Let ∠ ABC = ∠ ACB = y [∵AB = AC]
∴ ∠ BAC = 180° – 2y
⇒ ∠CAD = 180° – 2y
Also, ∠BAD = 180°
∴ 180° = (180° – 2y) × 2
⇒ 180° – 2y = 90°
⇒ 2y = 90° = ∠ BCD