In a Δ ABC, the bisectors of ∠ B and ∠ C intersect

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In a Δ ABC, the bisectors of ∠ B and ∠ C intersect each other at a point O. Then ∠ BOC is equal to :

In ΔABC, we know that ∠A + ∠B + ∠C = 180°

1	∠ A +	1	∠B +	1	∠C = 90°
2		2		2

1	∠A + ∠1 + ∠2 = 90°
2

∠1 + ∠2 = 90° -	1	∠A
	2

Now , In ΔBOC, ∠1 + ∠2 + ∠BOC = 180° ................ ( 1 )

	90° -	1	∠A		+ ∠BOC = 180° { using (i) }
		2

⇒ ∠BOC = 90° +	1	∠A
	2

120° +	1	∠A
	2

120° -	1	∠A
	2