Find out the value of ∠BAC.

60^{o}

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120^{o}

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90^{o}

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None of the above

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Solution

The correct option is A $60^{o}$

In the figure:
∠ACD = 120°

$Sum of adjacent angles = 180°$

So, ∠ACD + ∠ACB = 180°
⇒ 120° + ∠ACB = 180°
⇒ ∠ACB = 180° – 120° = 60°

By the angle sum property of a triangle:
∠ACB + ∠ABC + ∠BAC = 180°
⇒ 60° + 60° + ∠BAC = 180°
⇒ 120° + ∠BAC = 180°
⇒ ∠BAC = 180° – 120° = 60°

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