The internal bisectors of the angles B and C of a triangle

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The internal bisectors of the angles B and C of a triangle ABC meet at I. If ∠BIC = (∠A/2) + X, then X is equal to

1. 60°
2. 30°
3. 90°
4. 45°

Correct Option: C

On the basis of given in question , we draw a figure triangle ABC whose I is incentre ,

In ∆ ABC,
We know that , ∠A + ∠B + ∠ = 180°
∴ ∠B + ∠ = 180° – ∠A

∴		∠1	(∠B + ∠C) = 90° -	∠A
		2		2

In ∆ BIC,

		∠B	+	∠C	+ ∠BIC = 180°
		2		2

∴ 90° -		∠A	+ ∠BIC = 180°
		2

⇒ ∠BIC = 180° - 90° +		∠A
		2

∠BIC = 90° +		∠A
		2

∴ X = 90°