Question

In triangle ABC,angle ABC=angle ACB and the two bisectors of angle ABC and angle ACB intersect at O such that angle BOC=120degrees.Show that Angle A,B,C=60 degrees

Answer 1

$\mathbb{\pink{\huge{Hello\:Mate!!!}}}$

$<b><u>Answer</u></b>$

$<b>To prove ∠A, ∠B and ∠C = 60°</b>$

$<b><u>Step-by-step explanation</u></b>$

$<b>Given that,</b>$

∠ABC = ∠ACB

∠BOC = 120°

Divide on both sides by '2'.

$\frac{1}{2}$∠ACB = $\frac{1}{2}$∠ACB

=∠BOC = ∠OCB

$<b>Now,</b>$

∠BOC = 90° + $\frac{1}{2}$ ∠A

120° - 90° = $\frac{1}{2}$ ∠A

30° × 2 = ∠A

∠A = 60°

$<b>Now, in △ABC,</b>$

∠A + ∠ABC + ∠ACB = 180°

(Sum of all angles of a triangle)

= 60° + 2∠ABC = 180° (∵ ∠ABC = ∠ACB)

2∠ABC = 180° - 60°

= ∠ABC = $\frac{120°}{2}$ = 90°

= ∠ABC = ∠ACB (Given)

= ∴ ∠ABC = 60°

$<b>Hence, the proof</b>$

$<b>Happy New Year..!</b>$

Thanks...!

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Answer 2

The above answer is totally correct and could be referred to.

Hope it helps you guys :D