The problem asks to find the measure of angle $PNO$. We are given that the measure of angle $ONM$ is $68^\circ$ and the measure of angle $MNP$ is $33^\circ$.

1. Problem Description

The problem asks to find the measure of angle $PNO$. We are given that the measure of angle $ONM$ is $68^\circ$ and the measure of angle $MNP$ is $33^\circ$.

2. Solution Steps

We know that the angle $ONM$ is the sum of angles $ONP$ and $PNM$.

So, $m\angle ONM = m\angle ONP + m\angle PNM$.

We are given $m\angle ONM = 68^\circ$ and $m\angle PNM = 33^\circ$.

Therefore, we can write the equation as $68^\circ = m\angle ONP + 33^\circ$.

To find $m\angle ONP$, we subtract $33^\circ$ from both sides of the equation:

$m\angle ONP = 68^\circ - 33^\circ$.

$m\angle ONP = 35^\circ$.

The problem asks for $m\angle PNO$, which is the same as $m\angle ONP$.

3. Final Answer

35