Question

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

Answer 1

∠A = 60°

Step-by-step explanation:

Given:

Here in Δ ABC,the bisectors of ∠ABC and ∠ACB intersect at O.

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

So here, using the corollary, if the bisectors of ∠ABC and ∠ACB meet at a point O, then

$\angle BOC = 90 + \frac{1}{2}\angle A$

Therefore in Δ ABC,

$\angle BOC = 90 + \frac{1}{2}\angle A$

$120 = 90 + \frac{1}{2}\angle A$

$120 - 90 = \frac{1}{2}\angle A$

$30 = \frac{1}{2}\angle A$

$\angle A = 30 \times 2$

∠A = 60°

Answer 2

Answer:

∠A = 60°

Step-by-step explanation:

Given:

Here in Δ ABC,the bisectors of ∠ABC and ∠ACB intersect at O.

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

So here, using the corollary, if the bisectors of ∠ABC and ∠ACB meet at a point O, then

Therefore in Δ ABC,

∠A = 60°

Step-by-step explanation: