Question

In ABC, angle ABC =angle ACB and the by sector of angle ABC and ACB intersect at O such that angle BOC =120 degree. Show that angle A =angle = B= angle =C =360 degree ?

Answer 1

Answer:

Given In ∆ABC ∠ABC = ∠ACB Divide both sides by ‘2’

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

\begin{gathered}\frac{x}{2}+\frac{x}{2}+120=180\\\\implies x +120 = 180\\\\\implies x=60\degrees\end{gathered}

2

x

+

2

x

+120=180

impliesx+120=180

⟹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.