Internal bisectors of angles ∠B and ∠C of a triangle

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Internal bisectors of angles ∠B and ∠C of a triangle ABC meet at O. If ∠BAC = 80°, then the value of ∠BOC is

1. 120°
2. 140°
3. 110°
4. 130°

Correct Option: D

As per the given in question , we draw a figure of a triangle ABC in which ∠B and ∠C are internal bisectors of angles of triangle

Here , ∠BAC = 80°
In ∆ ABC ,
As we know that , ∠A + ∠B + ∠C = 180°
∴ ∠B + ∠C = 180° – 80° = 100°

	∠B	+	∠C	= 50°
	2		2

In ∆ BOC ,
⇒ ∠OBC + ∠OCB = 50°
∴ ∠BOC = 180° – 50° = 130°