Question

inABC. ir bisectors of LABC and LACB intersect at O at angle of 120°. then find the
measure of LA.​

Answer 1

Step-by-step explanation:

Answer

We have,

∠BOC=90

∘

+

2

1

∠A⇒120

∘

=90

∘

+

2

1

∠A⇒∠A=60

∘

∴∠A+∠B+∠C=180

∘

⇒60

∘

+2∠B=180

∘

[∵∠B=∠C(Given)]

⇒∠B=60

∘

Hence, ∠A=∠B=∠C=60

∘

answer verified by topper

Veeresh Gouda

Answer 2

Answer:

Step-by-step explanation:

Given:

Here in A 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

<BOC = 90+1/2 <A

Therefore in A ABC,

<BOC = 90+1/2<A

120 = 90+1/2<A

120-90= 1/2<A

30=1/2<A

< A = 30 × 2

<A = 60°