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To solve for the measure of angle \( x \) in the given figure, let's analyze the relationships between the angles provided:

1. **Observing the Angle Relationships**: 
   - The angles 122°, \( x \), and 156° are shown in the figure with intersecting lines.
   - The angle labeled \( x \) is adjacent to both 122° and 156°.

2. **Using Linear Pair Property**:
   - Since the angles on a straight line add up to 180°, we can set up an equation to find \( x \).
   - The angle \( x \) and 156° form a linear pair, meaning:
     \[
     x + 156^\circ = 180^\circ
     \]

3. **Calculating \( x \)**:
   \[
   x = 180^\circ - 156^\circ
   \]
   \[
   x = 24^\circ
   \]

4. **Conclusion**:
   - The measure of angle \( x \) is 24°.

So, the correct answer is:
- **C. 24°**

Would you like further details on the angle relationships, or have any other questions?

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### Additional Related Questions:
1. What is a linear pair of angles, and why do they add up to 180°?
2. How do vertical angles relate to each other in such a figure?
3. What is the sum of angles in a triangle, and how might that relate to solving for unknown angles?
4. How would you solve for unknown angles if given parallel lines cut by a transversal?
5. What other angle properties could apply in a similar diagram?

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**Tip**: When dealing with intersecting lines, always look for linear pairs or vertical angles as a way to simplify your calculations.

What is the measure of angle x if the angles are 122° and 156° as shown in the figure?

Learn how to find the measure of angle x in a linear pair given angles of 122° and 156°. This problem explores geometry concepts and the Linear Pair Theorem, ideal for 8th-grade students.

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