To find the missing angles in this diagram, we can apply basic principles from geometry, such as:

1. Vertical angles are equal (angles opposite each other when two lines cross).
2. Linear pair: The sum of angles on a straight line is $180^\circ$.

We have two sets of intersecting lines:

1. For angle $g$: Since angle $131^\circ$ and angle $g$ are a linear pair, we have: $g = 180^\circ - 131^\circ = 49^\circ$

2. For angle $h$: Angle $h$ is vertically opposite to the given angle $131^\circ$, so: $h = 131^\circ$

3. For angle $m$: Angle $m$ is vertically opposite to the given angle $54^\circ$, so: $m = 54^\circ$

4. For angle $k$: Since angle $54^\circ$ and angle $k$ are a linear pair, we have: $k = 180^\circ - 54^\circ = 126^\circ$

Final Answers:

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

Would you like any further details or explanations?

Here are five related questions to expand your understanding:

1. What are vertical angles, and why are they always equal?
2. How can you identify a linear pair of angles in a diagram?
3. How would the solution change if the given angles were supplementary instead of vertical?
4. How do parallel lines affect angle relationships in similar problems?
5. How does knowing that the sum of angles around a point is $360^\circ$ help solve more complex problems?

Tip: When dealing with intersecting lines, always check for vertical angles and linear pairs to simplify your calculations.