In the given figure, in ΔABC, the angle bisectors of ∠B and ∠C meet at a point O. Find the measure of ∠BOC.
Given, ∠A = 70°
Let the two angles ∠B = 2x and ∠C = 2y.
Then, angle bisector of B, ∠OBC = x and angle bisector of C, ∠OCB = y
⸫ ∠A + ∠B + ∠C = 180° [Sum of all angles of a triangle = 180°]
⇒ 70° + 2x + 2y = 180°
⇒ 2x + 2y = 110°
⸫ x + y = 55° …. (i)
Now,
∠BOC + x + y = 180° [Sum of all angles of a triangle = 180°]
⇒ ∠BOC = 180° - (x + y)
⇒ ∠BOC = 180° - 55° [from eq. (i)]
⸫ ∠BOC = 125°