The internal bisectors of ∠ABC and ∠ACB of ∆ABC

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The internal bisectors of ∠ABC and ∠ACB of ∆ABC meet each other at O. If ∠BOC =110°, then ∠BAC is equal to

1. 40°
2. 55°
3. 90°
4. 110°

Correct Option: A

On the basis of question we draw a figure of a ∆ABC in which the internal bisectors of ∠ABC and ∠ACB meet each other at O ,

In ∆ ABC,
∠A + ∠B + ∠C = 180° ... (i)
In ∆ OBC,
We have , ∠OBC + ∠BOC + ∠OCB = 180°

⇒	∠B	+ 110° +	∠C	= 180°
	2		2

⇒	∠B + ∠C	= 180° - 110° = 70°
	2

⇒ ∠B + ∠C = 140°
From (i) , we get
∴ ∠A = 180° – 140° = 40°