The diagram you've provided shows two intersecting lines with angles marked. We can use the properties of vertical angles and linear pairs to find the missing angle measures.

1. Vertical angles are congruent. So:

   • $g$ and the given $131^\circ$ angle are vertical angles, meaning $g = 131^\circ$.
   • Similarly, $k$ and the given $54^\circ$ angle are vertical angles, so $k = 54^\circ$.

2. Linear pairs (angles on a straight line) sum up to $180^\circ$. So:

   • $h + 131^\circ = 180^\circ$, which gives $h = 180^\circ - 131^\circ = 49^\circ$.
   • $m + 54^\circ = 180^\circ$, which gives $m = 180^\circ - 54^\circ = 126^\circ$.

Thus, the missing angle measures are:

• $g = 131^\circ$
• $h = 49^\circ$
• $k = 54^\circ$
• $m = 126^\circ$

Would you like a further explanation or details about this process?

Here are 5 related questions to expand this concept:

1. How can you use the concept of supplementary angles to solve more complex diagrams?
2. What are alternate interior angles and how can they help in such problems?
3. How do parallel lines affect the angle relationships in these kinds of problems?
4. What is the difference between complementary and supplementary angles?
5. How can angle bisectors change the relationships between angles?

Tip: Always remember that vertical angles are congruent and adjacent angles on a straight line are supplementary.