Comparing Angles in an Equilateral Triangle: Which is Larger, ∢B or ∢A?

In this problem, we need to determine which angle is larger between $∢B$ and $∢A$ in the equilateral triangle $\triangle ABC$.

Let's start by recalling what an equilateral triangle is. In an equilateral triangle, all three sides have equal length, and consequently, all three internal angles are of equal measure. This is a fundamental property of equilateral triangles.

Since $\triangle ABC$ is equilateral, we know that each angle, including $∢B$ and $∢A$, measures $60^\circ$. This is because the sum of internal angles in any triangle is $180^\circ$, and in an equilateral triangle, this total is divided equally among the three angles. Thus:
$\begin{aligned} ∢A &= ∢B = ∢C = \frac{180^\circ}{3} = 60^\circ. \end{aligned}$

Since both $∢A$ and $∢B$ are $60^\circ$, neither angle is larger than the other; they are equal.

This means that the correct statement regarding their measures is that $∢A = ∢B$.

Thus, according to the choices provided, the correct answer is:

Choice 4: $∢A = ∢B$.