In triangle ABC, bisector of ∠ABC and ∠ACB meet at O. If ∠BAC=60°, then find the measure of ∠BOC.

Correct option is A

Given:

In $$\triangle ABC$$​, the bisectors of $$\angle ABC$$​ and $$\angle ACB$$​ meet at point O . It is given that $$\angle BAC = 60^\circ$$​ . We need to find the measure of $$\angle BOC$$​ .

Theorem Used

In a triangle, if two angle bisectors intersect at a point, that point divides the included angle between the other two vertices. For a triangle $$\triangle ABC$$​ with internal angles A, B, and C , the measure of the angle at the intersection of the bisectors of B and C ($$i.e., \angle BOC$$​) is given by:
​$$\angle BOC = 90^\circ + \frac{\angle BAC}{2}$$​​

Solution

Substitute the value of $$\angle BAC = 60^\circ$$​ into the formula:
​$$\angle BOC = 90^\circ + \frac{60^\circ}{2}\\\ \\\angle BOC = 90^\circ + 30^\circ = 120^\circ$$​​

The measure of $$\angle BOC \ is \ 120^\circ$$​ .