Question

In triangle ABC ,if bisectors of <ABC and < ACB intersect at O at an angle
of 120 0 . Then find the measure of <A.

Answer 1

Answer:

Given:

Here in A ABC, the bisectors of ZABC and ZACB intersect at O.

Also as shown in the figure, <BOC = 120°

So here, using the corollary, if the bisectors of ZABC and ZACB meet at a point O, then

ZBOC= 90+ZA

Therefore in A ABC,

ZBOC= 90+ZA

120 - 90+ZA 2

120- 90 ZA

30 = A -

ZA = 30 × 2

ZA = 60°

Answer 2

Answer:

In ΔBQC

∠BOC + ∠OBC + ∠OCB = 180°

$120° + \frac{1}{2} ∠B + \frac{1}{2} ∠C = 180°$

$\frac{1}{2} (∠B + ∠C)=60°$

∠B + ∠C = 120° (i)

In ΔABC

∠A + ∠B + ∠C = 180°

∠A + 120° = 180°[From (i)]

∠A = 60°