Identify angles related to the diameter.

Since $LOM$ is a diameter, the angle subtended by the diameter at any point on the circumference is $90^\circ$.
Therefore, $\angle LTM = 90^\circ$ (angle in a semicircle).

Since $LT$ is produced to $P$, $L, T, P$ are collinear.
Thus, $\angle PTM = \angle LTM = 90^\circ$. This is an angle of the quadrilateral $MNPT$.

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