# In a triangle ABC, ∠B = 60° and ∠C = 80°. Suppose the bisector of ∠B and ∠C meet at I. Find ∠BIC.

It is given that in a triangle ABC, B = 60°, and C = 80°. IB and IC are the bisectors of B and C respectively.

⇒ ∠IBC = 30° and ICB = 40°

We know that the sum of the angles of a triangle is 180°.

So, in ∆ IBC

⇒ ∠BIC + IBC + ICB = 180°

⇒ ∠BIC = 180° - 40° - 30°

⇒ ∠BIC = 110°

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