Institution: Bangladesh Development Bank Exam: Bangladesh Development Bank Ltd - Senior Officer - 24.11.2017
Topic: Arithmetic Mathematics (পাটিগণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

In triangle ABC, the relationship between the lengths of the sides and the measures of the angles is governed by the Triangle Inequality Theorem, which states that the largest angle is opposite the longest side.

In this case, we know that side AB is greater than side AC (AB > AC). According to the theorem, the angle opposite AB (which is ∠ ACB) must be larger than the angle opposite AC (which is ∠ ABC). This leads us to conclude that:

1. Since AB > AC, it follows that ∠ ACB > ∠ ABC.
2. Consequently, ∠ ABC, which is opposite side AC, will be smaller than ∠ ACB, confirming that ∠ ABC < ∠ ACB.

Now, let's examine the provided options. The correct conclusion is reflected in option A: ∠ ABC > ∠ ACB. However, since it contradicts our deductions, the correct interpretation of the conditions suggests option D (∠ ACB > ∠ ABC) is technically the conclusion we arrived at.

Thus, the correct statement based on the relationship of the angles and sides in triangle ABC is:
**D)** ∠ ACB > ∠ ABC.

This understanding emphasizes the importance of angle-side relationships in triangles.