SSC CPO 2020 PYQ — Question 110

The correct answer is option 4 i.e. 104°

In ΔABC, the bisectors of ∠B and ∠C meet at M.

If ∠BOC = 142⁰

The sum of three angles of a triangle is 180⁰

The bisector of an angle bisects the angle in two equal parts.

Let, ∠B = x and ∠C = y

OB and OC are two angle bisectors and meet at M.

In ΔBCM -

(x/2) + (y/2) + 142⁰ = 180⁰

(x/2) + (y/2) = 38⁰

x + y = 76⁰

In ΔABC -

∠B + ∠C = 76⁰

∠A = 180⁰ - 76⁰

∠A = 104⁰