Question

ABC is a triangle in which ∠A = 72°, the internal bisectors of angles B and C meet in O. Find the magnitude of ∠BOC.

Answer 1

The magnitude of ∠BOC is 126°

Step-by-step explanation:

• Given data

        ∠A = 72°

• Here ABC is a triangle

• When internal angle bisector of two vertices B and C meet at point O, There are relation between ∠BOC and ∠A are given below

        $\mathbf{\angle BOC =90 + \frac{\angle A}{2}}$

        So

        $\mathbf{\angle BOC =90 + \frac{72}{2}}$

        $\mathbf{\angle BOC =90 + 36=126^{\circ}}$

     

• There are some extra formula when external angle bisector of two vertices B and C meet at point O, There are relation between ∠BOC and ∠A are given below

        $\mathbf{\angle BOC =90 - \frac{\angle A}{2}}$