O is the in-centre of the ∆ABC, if ∠BOC = 116°,

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O is the in-centre of the ∆ABC, if ∠BOC = 116°, then ∠BAC is

1. 42°
2. 62°
3. 58°
4. 52°

Correct Option: D

On the basis of given in question , we draw a figure triangle ABC in which O is the in-centre ,

The point of intersection of internal bisectors of a triangle is called in-centre.

∠BOC = 90° +	∠A
	2

⇒ 116° = 90° +	∠A
	2

⇒	∠A	= 116° - 90° = 26°
	2

∴ ∠A = 26 × 2 = 52°