Answer
$C = 77.1^{\circ}$
Work Step by Step
We can use the law of cosines to find $C$:
$AB^2 = AC^2+BC^2-2(AC)(BC)~cos~C$
$2(AC)(BC)~cos~C = AC^2+BC^2-AB^2$
$cos~C = \frac{AC^2+BC^2-AB^2}{2(AC)(BC)}$
$C = arccos(\frac{AC^2+BC^2-AB^2}{2(AC)(BC)})$
$C = arccos(\frac{102^2+135^2-150^2}{2(102)(135)})$
$C = arccos(0.2225)$
$C = 77.1^{\circ}$