Question

In ∆ABC, if ∠ABC = ∠BAC + ∠ACB, the value

of ∠ABC is

Answer 1

we know sum of angles in a triangle is 180.
given,
angle ABC =angle BAC+angle ACB.

so, angle ABC+angle BAC+angle ACB=180.
angle BAC + angle ACB +angle BAC+angle ACB=180

2 angle BAC+ 2angle ACB =180
2(angle BAC +angle ACB)=180.

angle BAC+angle ACB=180/2=90

such that angle ABC 90.

hope this answer helps u....

Answer 2

Since sum of all the 3 angles in a triangle is 180.
and it is given that,
∠ABC =∠BAC+∠ ACB.

∴ ∠ABC+∠BAC+∠ACB=180.
∴∠BAC +∠ACB +∠BAC+∠ACB=180

∴ 2∠BAC+ 2∠ACB =180
2{∠BAC +∠ACB}=180.

∴∠BAC+∠ACB ⇒180/2=90

∴ ∠ABC 90.