Question

in a triangle ABC angle ABC is equal to angle ACB and the bisectors of angle ACB and ABC intersect at O such that angle BOC is equal to 120 degree show that angle is equal to angle b is equal to angle C is equal to 60 degree

Answer 1

Answer:

The proof is explained step wise below :

Step-by-step explanation:

For better understanding of the solution see the attached figure of the diagram :

In ΔABC, By using angle sum property of a triangle

x + x + z = 180°

2·x + z = 180°   .........(1)

In ΔAOB , By using angle sum property of a triangle

$\frac{x}{2}+\frac{x}{2}+120=180\\\\implies x +120 = 180\\\\\implies x=60\degrees$

Now, using equation (1)

2 × 60 + z = 180°

⇒ z = 60°

Hence, m∠ABC = x = 60°

m∠ACB = x = 60°

m∠BAC = z = 60°

SO, all the angles are of 60° each.

Hence Proved.