Question

In ΔABC, if bisectors of ∠ABC and ∠ACB intersect at O at angle of 120°, then find the measure of ∠A.

Answer 1

In the given ΔABC, ∠ABC = ∠ACB, the bisectors of ∠ABC and ∠ACBmeet at O and ∠BOC = 120°

We need to find the measure of ∠A

So here, using the corollary, “if the bisectors of ∠ABCand ∠ACBof a ΔABCmeet at a point O, then`∠BOC = 90° + 1/2 ∠A`

Thus, in ΔABC

`∠BOC = 90° + 1/2 ∠A`

` 120°  = 90° + 1/2 ∠A`

`120° - 90° + 1/2 ∠A`

∠A = 2(30°)

∠A= 60°

Thus, ∠A = 60°