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To solve this problem, we can apply properties of angles formed by intersecting lines. Specifically, we use the following properties:

1. **Vertically opposite angles** are equal.
2. **Linear pairs** of angles (angles on a straight line) sum to 180°.

Let’s find the missing angles step by step.

### Step 1: Find angle \( g \)
Angle \( g \) is vertically opposite to the given angle of \( 131^\circ \), so:
\[
g = 131^\circ
\]

### Step 2: Find angle \( h \)
Angles \( h \) and \( 131^\circ \) form a linear pair (they are on the same straight line), meaning they must sum to \( 180^\circ \). So:
\[
h = 180^\circ - 131^\circ = 49^\circ
\]

### Step 3: Find angle \( m \)
Angle \( m \) is vertically opposite to the given angle of \( 54^\circ \), so:
\[
m = 54^\circ
\]

### Step 4: Find angle \( k \)
Angles \( k \) and \( 54^\circ \) form a linear pair, so they must sum to \( 180^\circ \). Thus:
\[
k = 180^\circ - 54^\circ = 126^\circ
\]

### Final Answers:
- \( h = 49^\circ \)
- \( g = 131^\circ \)
- \( m = 54^\circ \)
- \( k = 126^\circ \)

Would you like any further details or clarification?

### 5 Related Questions:
1. What are supplementary angles, and how do they relate to linear pairs?
2. How can we find missing angles when given a transversal line across parallel lines?
3. What are corresponding angles, and how are they used in geometry?
4. Can two vertically opposite angles ever not be equal?
5. How would the solution change if one of the intersecting lines was not straight?

### Tip:
When working with intersecting lines, always look for vertically opposite angles and linear pairs to simplify the problem quickly.

This question focuses on finding the missing angles in a set of intersecting lines using vertically opposite angles and linear pair properties. In this step-by-step solution, learn how to calculate the angles when some values are given.

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