$\because$点$O$是矩形$ABCD$的对称中心，
$\therefore OA=OB$，
$\therefore \angle OAB=\angle OBA$.
$\because$四边形$ABCD$是矩形，
$\therefore \angle BAD=90^{\circ}$.
$\because \angle OAD=20^{\circ}$，
$\therefore \angle OAB=90^{\circ}-20^{\circ}=70^{\circ}$，
$\therefore \angle OBA=70^{\circ}$.
故答案为：$70$.

$\because$点$O$是矩形$ABCD$的对称中心，
$\therefore OA=OB$，
$\therefore \angle OAB=\angle OBA$.
$\because$四边形$ABCD$是矩形，
$\therefore \angle BAD=90^{\circ}$.
$\because \angle OAD=20^{\circ}$，
$\therefore \angle OAB=90^{\circ}-20^{\circ}=70^{\circ}$，
$\therefore \angle OBA=70^{\circ}$.
故答案为：$70$.