Q12 of 34 Page 170

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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