Answer
measure of arc $AB=144^{\circ}$
Work Step by Step
The measure of a circle is $360^{\circ}$. Also, if two chords are congruent, then their arcs are congruent. Since $\overline{AB}=\overline{AC}$, their arcs are congruent. From part a we know that the measure of arc $BC=72^{\circ}$. Subtract the known arc from $360$, then divide the resulting number by 2 (for the two congruent arcs)...
$360-72=288\div2=144$
measure of arc $AB=144^{\circ}$