ABC is an isosceles triangle with AB AC The side BA is produced to D such that AB AD If ang ABC 30 d...........

Quantitative Aptitude ( CCS) Geometry

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

45°

90°

30°

60°

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Explanation:

AB = AC = AD
∠ACB = ∠ABC = 30°
We know that, Exterior angle is equal to the sum of two interior opposite angles
∴ ∠DAC = ∠ABC + ∠ACB = 30° + 30° = 60°
In ΔACD,
AC = AD
∠ADC = ∠ACD
We know that,
∠ACD + ∠ADC + ∠DAC = 180°
∠ACD + ∠ACD + 60° = 180° [? ∠ACD = ∠ADC]
2∠ACD = 180° – 60° = 120°
∠ACD = 60°
Required angle, ∠BCD = ∠ACB + ∠ACD = 30° + 60° = 90°