Let's look at the detailed solution of the above problem

Steps 1 & 2: Understand Question and Draw InferencesGiven ABC is a triangle.

Since we don’t have any other information, let’s move on to the analysis of the statement 1.

Step 3: Analyze Statement 1 independentlyStatement 1 tells us that \(∠ABC = ∠ACB\)

From this we can conclude that ABC is an isosceles triangle and we do not have sufficient information to conclude that ABC will be an equilateral triangle.

So statement 1 is not sufficient to arrive at a unique answer.Step 4: Analyze Statement 2 independentlyStatement 2 says: Length of AB = Length of AC and one of the angles of the triangle is 60o

If length AB = length AC, then we can conclude that –

\(∠ABC = ∠ACB\)

And it is also given that one of the angles is \(60^o\).

So there are two possibilities –

Case 1: \(∠ABC = ∠ACB = 60^o\)

If this is the case, then the third angle i.e. ∠BAC will automatically become \(60^o\).

Since the sum of internal angles must be equal to \(180^o\).

Case 2:\(∠BAC = 60^o\)

The remaining \(120^o\) angle has to be split equally between ∠ABC and ∠ACB as they equal.

This makes all angles equal to \(60^o\) each.

Thus, in both cases we find that ABC is an equilateral triangle.

Therefore, statement 2 is sufficient to arrive at a unique answer. Hence the correct Answer is B.
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