UKMT Senior Mathematical Challenge, 2015

A circle touches the sides of triangle $PQR$ at the points $S$, $T$ and $U$ as shown. Also $\angle PQR = \alpha°$, $\angle PRQ = \beta°$ and $\angle TSU = \gamma°$. Which of the following gives $\gamma$ in terms of $\alpha$ and $\beta$?

(A) $\frac{1}{2}(\alpha+\beta)$ (B) $180 - \frac{1}{2}(\alpha+\beta)$ (C) $180 - (\alpha+\beta)$ (D) $\alpha+\beta$ (E) $\frac{1}{3}(\alpha+\beta)$