Answer
$30 ^\circ$
Work Step by Step
Consider $p$ be the measure of the angle with equal measure for two angles.
Thus, $120 ^\circ +p+p=180 ^\circ$
$120 ^\circ +2p=180 ^\circ$
$2p=180 ^\circ-120 ^\circ$
$2p=60^\circ$
$p=30 ^\circ$