In ΔABC, AC > AB. D is any point on the side AC such that ∠ADB = ∠ABD. Let’s prove that ∠ABC > ∠ACB.

Given: ΔABC, AC > AB, D is point on the side AC such that ∠ADB = ∠ABD

To prove: ∠ABC > ∠ACB

The figure for the given question is as shown below,

In the given ΔABC,

∠ABC is opposite to side AC,

And also ∠ACB is opposite to the side AB.

And given AC > AB

We know in a triangle the shortest side is always opposite the smallest interior angle and the longest side is always opposite the largest interior angle.

⇒ ∠ABC > ∠ACB

Hence proved