In the given diagram, the question asks to identify a pair of adjacent angles.

Explanation:

• Adjacent angles are two angles that share a common side and a common vertex but do not overlap.
• In the diagram, angles $\angle ABD$, $\angle BDC$, and $\angle BDE$ are marked.

Let’s analyze the provided answer choices:

1. $\angle ABD$ and $\angle BDE$: These angles are not adjacent because they do not share a common side.
2. $\angle ABD$ and $\angle BDC$: These two angles are adjacent. They share the side $BD$ and the vertex $B$.
3. $\angle BDC$ and $\angle BDE$: These angles are adjacent, as they share the side $BD$ and the vertex $D$.

Thus, the correct answer is the second option: $\angle ABD$ and $\angle BDC$.

Would you like further details or explanations?

Here are five related questions:

1. What are supplementary angles, and are any pairs supplementary in this diagram?
2. Can adjacent angles also be complementary?
3. How do you determine if two angles are vertically opposite?
4. What is the sum of angles around point $D$?
5. How would you calculate an unknown angle if one angle measure was missing?

Tip: When identifying adjacent angles, always check for a shared side and vertex without overlapping.