$\begin{align}  & \angle QOP={{125}^{\circ }} \\ & \angle PON={{180}^{\circ }}-{{125}^{\circ }}={{55}^{\circ }}\text{ } \\ & \text{ }\!\!\{\!\!\text{ }\angle s\text{ on a straight line }\!\!\}\!\!\text{ } \\ & \angle MNO=\angle PON={{65}^{\circ }}\text{  }\!\!\{\!\!\text{ alternate angles }\!\!\}\!\!\text{ } \\ & \text{In }\vartriangle MNQ \\ & \angle QMN+\angle MNQ+\angle MQN={{180}^{\circ }} \\ & {{65}^{\circ }}+{{55}^{\circ }}+\angle MQN={{180}^{\circ }} \\ & \angle MQN={{60}^{\circ }} \\ & \angle MQN+\angle MQR={{180}^{\circ }} \\ & \angle MQR={{180}^{\circ }}-{{60}^{\circ }}={{120}^{\circ }} \\\end{align}$