O is the incentre of the triangle ABC. If ∠BOC = 110°, then ∠BAC is

As the incentre is formed by joining angle bisectors of ∠A, ∠B and ∠C of a triangle ABC,

∴ In ΔOBC,

By Angle Sum Property,

∠BOC + ½ ∠ABC + ½ ∠ACB = 180°

⇒ ½ (∠ABC + ∠ACB) = 180° – 110° = 70°

⇒ ∠ABC + ∠ACB = 140° ---(1)

In ΔABC,

By Angle Sum Property,

∠BAC + ∠ABC + ∠ACB = 180°

From 1,

∠BAC + 140° = 180°

∴ ∠BAC = 40°.