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The problem is asking to identify which of the given diagrams shows adjacent angles \( \angle ABC \) and \( \angle CBD \).

### Explanation:
- **Adjacent angles** share a common vertex and a common side (ray), but they do not overlap.
- In this case, \( \angle ABC \) and \( \angle CBD \) must:
  1. Share the vertex \( B \),
  2. Share the side \( BC \),
  3. Have distinct other sides (rays) like \( AB \) and \( BD \).

Looking at the diagrams:
- **First diagram**: The angles \( \angle ABC \) and \( \angle CBD \) seem to be adjacent because:
  - They share the vertex \( B \),
  - They share the common side \( BC \),
  - Their other sides are \( AB \) and \( BD \), respectively.

Thus, the **first diagram** shows adjacent angles \( \angle ABC \) and \( \angle CBD \).

Would you like more details on this concept, or do you have any further questions?

### Related Questions:
1. What are supplementary angles, and how are they related to adjacent angles?
2. Can adjacent angles be complementary?
3. How do vertical angles differ from adjacent angles?
4. What is the importance of adjacent angles in geometry?
5. How can you calculate the sum of adjacent angles if they form a straight line?

### Tip:
Adjacent angles that form a straight line are called *linear pairs* and are always supplementary.

Which of the following shows adjacent angles ABC and CBD?

Learn how to identify adjacent angles ABC and CBD in a geometry diagram. This problem explains the concept of adjacent angles, which share a common vertex and a common side. Suitable for students in Grades 6-8.

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