In the image, we see a lamp with two intersecting metal bars, forming angles at the intersection point labeled as $B$.

Adjacent Angles:

Adjacent angles are pairs of angles that share a common vertex and a common side, but do not overlap.

The metal bars intersect at $B$, creating the following angles:

• $\angle ABE$
• $\angle CBE$
• $\angle ABD$
• $\angle DBC$

Now let's list the adjacent angle pairs based on these observations:

1. $\angle ABE$ and $\angle CBE$ (sharing side $BE$)
2. $\angle ABD$ and $\angle DBC$ (sharing side $BD$)

Thus, there are 2 pairs of adjacent angles in the figure.

Would you like more details, or do you have any other questions?

Here are 5 related questions to expand your understanding:

1. What is the definition of supplementary angles, and can you identify any pairs in the diagram?
2. What other geometric properties can be inferred from the intersection of these two bars?
3. How would the situation change if another bar were added to the figure?
4. Can vertical angles be formed in this situation? How many pairs are there?
5. How do adjacent angles relate to linear pairs?

Tip: When two lines intersect, the adjacent angles formed are often supplementary, summing to $180^\circ$.