$\displaystyle\angle{P}{U}{T}\usepackage{cmbright}\Huge\$ is a straight angle, so it measures $\displaystyle{{180}}^{\circ}\usepackage{cmbright}\Huge\$ . The four angles along this straight angle have measures that total $\displaystyle{{180}}^{\circ}\usepackage{cmbright}\Huge\$ . So:

$\displaystyle{m}\angle{P}{U}{Q}+{{49}}^{\circ}+{{52}}^{\circ}+{{36}}^{\circ}={{180}}^{\circ}\usepackage{cmbright}\Huge\$

$\displaystyle{m}\angle{P}{U}{Q}={{180}}^{\circ}-{\left({{49}}^{\circ}+{{52}}^{\circ}+{{36}}^{\circ}\right)}={{43}}^{\circ}\usepackage{cmbright}\Huge\$