To solve this problem, we'll use the exterior angle theorem. This theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.

Given:

• $\angle NPO = 38^\circ$
• $\angle PON = 39^\circ$
• $\angle PNM = x^\circ$ (exterior angle)

Using the exterior angle theorem: $x = \angle NPO + \angle PON$ Substituting the given values: $x = 38^\circ + 39^\circ = 77^\circ$

So, $x = 77^\circ$.

Now, let's analyze the statements:

1. $x > 38$ — True, because $77 > 38$.
2. $x < 39$ — False, because $77 > 39$.
3. $x < 77$ — False, because $x = 77$.
4. $x > 103$ — False, because $77 < 103$.

The correct statement is $x > 38$.

Would you like more details or have any questions? Here are some related questions to consider:

1. How does the exterior angle theorem help in triangle problems?
2. Can an exterior angle of a triangle be equal to one of its interior angles?
3. What is the sum of all interior angles of a triangle?
4. How can you prove the exterior angle theorem?
5. What would happen if $\angle PON$ was greater than $\angle NPO$?

Tip: Remember, the exterior angle theorem is a powerful tool for solving triangle-related problems and finding unknown angles.