A quadrilateral MNOP is inscribed in a circle. If MN is a diameter, what can you say about $\angle MOP$ and $\angle MNP$? Explain your reasoning.

Let $\angle MOP = x$ and $\angle MNP = y$

Since MN is a diameter,

$\angle MPN = \angle MON = 90^\circ$[Angle in semicircle] ...(i)

Now, in cyclic quadrilateral MNOP,

$\angle NOP + \angle NMP = 180^\circ$

But $\angle NOP = \angle NOM + \angle MOP = 90^\circ + x$

Hence, $90^\circ + x + \angle NMP = 180^\circ$

$\angle NMP = 90^\circ - x$ ...(ii)

In $\triangle MNP$,

$\angle NMP + \angle MPN + \angle MNP = 180^\circ$.                  [Angle sum property]

Substituting,

$(90^\circ - x) + 90^\circ + y = 180^\circ$       [From (i) and (ii)]

$y = x$
 Therefore, $\angle MOP = \angle MNP$.