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∆ ABC is an isosceles triangle in which AB = AC. Side BA is extended to D such that AB = AD. What will be the value of∠BCD ?
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- 90°
- 60°
- 30°
- 45°
- 90°
Correct Option: A
As per the given in question , we draw a figure an isosceles triangle ABC in which AB = AC and side BA is extended to D such that AB = AD
In ∆ ABC,
AB = AC
⇒ ∠ACB = ∠ABC ..... (i)
Now, AB = AD
∴ AD = AC
In ∆ ADC,
AD = AC
⇒ ∠ACD = ∠ADC ....(ii)
By equations (i) + (ii),
∠ACB + ∠ACD = ∠ABC + ∠ADC
⇒∠BCD = ∠ABC + ∠BDC
⇒∠BCD + ∠BCD = ∠ABC + ∠BDC + ∠BCD
⇒ 2 ∠BCD = 180°
⇒∠BCD = 90°
