Answer
$a)30^0$
$b)120^0$
Work Step by Step
If two angles are Complement then sum of these angles is $90^0$
If two angles are Supplement then sum of these angles is $180^0$
$a)\alpha+60^0=90^0\Rightarrow \alpha =90^{0}-60^{0}=30^{0};$
$b)\theta+60^0=180^0\Rightarrow \theta=180^{0}-60^{0}=120^{0}$