The internal bisectors of the ∠B and ∠C of the ∆

Home » Aptitude » Plane Geometry » Question

The internal bisectors of the ∠B and ∠C of the ∆ ABC, intersect at O. If ∠A = 100°, then the measure of ∠BOC is :

On the basis of given in question , we draw a figure triangle ABC ,

∠OBC =	1	∠ABC;
	2

∠OCB =	1	∠ACB;
	2

From ∆ OBC,
∠OBC + ∠OCB + ∠BOC = 180°

	1	(∠ABC + ∠ACB) + ∠BOC = 180°
	2

⇒	1	(180° - ∠BAC) + ∠BOC = 180°
	2

⇒	1	(180° - 100) + ∠BOC = 180°
	2

⇒ ∠BOC = 180° – 40° = 140°