To solve for $m \angle MNO$, we can use the following approach:

Step-by-Step Solution

1. Identify Known Angles:

   • We know that $m \angle MNP = 53^\circ$.
   • We also know that $m \angle PNO = 36^\circ$.

2. Recognize the Relationship Between the Angles:

   • Since $MNP$ and $PNO$ are adjacent angles that share the common point $N$ and lie along the line segment $NO$, they together form the angle $MNO$.
   • Therefore, $m \angle MNO = m \angle MNP + m \angle PNO$.

3. Calculate $m \angle MNO$: $m \angle MNO = 53^\circ + 36^\circ = 89^\circ$

Conclusion

Thus, $m \angle MNO = 89^\circ$.

Would you like more details on any step or have any questions?

Here are five related questions to deepen your understanding:

1. How would the solution change if $m \angle MNP$ or $m \angle PNO$ was different?
2. What if there was a third angle between $N$ and $O$ along the line—how would that affect $m \angle MNO$?
3. How can we verify if $N$, $P$, and $O$ lie in a straight line?
4. Why do we add angles $m \angle MNP$ and $m \angle PNO$ to find $m \angle MNO$?
5. What is the sum of angles around a point like $N$ in general, and why?

Tip: Remember that adjacent angles along a straight line add up to $180^\circ$.