Since MNOP is inscribed in a circle with vertices in order M, N, O, P, and MN is a diameter, both O and N lie on the same arc (the major arc MP). The angles $\angle MOP$ and $\angle MNP$ are both inscribed angles subtended by the same chord MP from the same segment of the circle. By the Inscribed Angle Theorem, inscribed angles subtended by the same chord from the same segment are equal. Therefore, $\angle MOP = \angle MNP$. Note that $\angle MOP$ is the angle at O between diagonal OM and side OP, and $\angle MNP$ is the angle at N between side NM and diagonal NP — these are not the interior opposite angles of the cyclic quadrilateral. The fact that MN is a diameter is extra information that does not alter this relationship.