In ∆ABC, the external bisectors of the angles ∠B

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In ∆ABC, the external bisectors of the angles ∠B and ∠C meet at the point O. If ∠A = 70°, then the measure of ∠BOC is :

1. 55°
2. 75°
3. 60°
4. 50°

Correct Option: A

According to question , we draw a figure

The sides AB and AC of a triangle ∆ ABC are produced to P and Q respectively. If the bisectors of ∠PBC and ∠QCB interest at O, then

∠BOC = 90° -	1	∠A
	2

Here, ∠A = 70°

∴ ∠BOC = 90° -	70°
	2

∠BOC = 90° – 35° = 55°