Question

In an isosceles ∆ABC, the bisectors of ∠B and ∠C meet at a point O. If ∠A = 40°, then ∠BOC =
?
(a) 110°
(b) 70°
(c) 130°
(d) 150°

Answer 1

Correct option: (a)

In the isosceles ABC, ​the bisectors of ∠B and ∠C meet at point O.
Since the triangle is isosceles, the angles opposite to the equal sides are equal.
∠B = ∠C
$\therefore$ ∠A + ∠B + ∠C = 180^o
⇒ 40^o + 2∠B = 180^o
⇒ 2∠B = 140^o
⇒ ∠B = 70^o
Bisectors of an angle divide the angle into two equal angles.
So, in ∆BOC:
∠OBC = 35^o and ∠OCB = 35^o
∠BOC + ∠OBC + ∠OCB = 180​^o
⇒ ∠BOC + 35^o + 35^o = 180^o
⇒ ∠BOC = 180^o​ - 70^o
⇒ ∠BOC = 110^o