In ABC, BC = AB and B = 80^. Then A is equal to

Given that in $\triangle ABC$, $BC = AB$, this means that $\triangle ABC$ is an isosceles triangle.

In an isosceles triangle, the angles opposite the equal sides are equal. Since side BC is opposite $\angle A$ and side AB is opposite $\angle C$, we have $\angle A = \angle C$.

The sum of the interior angles in any triangle is $180^\circ$.
So, $\angle A + \angle B + \angle C = 180^\circ$.

We are given $\angle B = 80^\circ$. Since $\angle A = \angle C$, we can substitute $\angle A$ for $\angle C$ in the equation:

The final answer is \boxed{\text{50^\circ}}.