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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.

Find the measure of the missing angles. The angles given are 131° and 54° in a vertical line intersected by two diagonal lines, creating angles g, h, m, and k.

Learn how to find the missing angles in an intersecting lines diagram using vertical angles and linear pairs. Understand the properties of vertical and supplementary angles to solve problems like the one shown, with given angles 131° and 54°. Suitable for students in Grades 7-8.

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