Answer
$m\angle ABC=72^{\circ}$
Work Step by Step
We are given that chords $AB$ and $AC$ are congruent. Therefore, $\triangle ABC$ is an isosceles triangle. Also, we found that the $m\angle A=36^{\circ}$. Subtract the vertex angle from $180$ and divide the resulting number by two (the two base angles) and we will find the $m\angle ABC$.
$180-36=144\div2=72$
$m\angle ABC=72^{\circ}$