#### Answer

$ 75^{\circ}$

#### Work Step by Step

we know sum of all three angles of triangle is $180^ {\circ}$
$m\angle A + m\angle B + m \angle C $= $180 ^ {\circ} $
$63^{\circ}+ 42^{\circ}+ \angle C$ =$ 180^{\circ}$
$105^{\circ}+\angle C$ = $180^{\circ}$
$ \angle C$ = $180^{\circ}-105^{\circ}$
$\angle C$ = $75^{\circ}$