To find a pair of adjacent complementary angles in the given figure, we need to identify two angles that:

1. Are adjacent (they share a common vertex and side).
2. Add up to 90° (since complementary angles sum to 90°).

Right Side of the Figure:

• Angles $\angle LJM$ and $\angle MJN$ are adjacent.
• Their measures are $56^\circ$ and $34^\circ$ respectively.
• $56^\circ + 34^\circ = 90^\circ$, so they are complementary.

Thus, the pair of adjacent complementary angles is: $\boxed{\angle LJM \text{ and } \angle MJN}.$

Would you like a detailed explanation of how complementary angles work or more information?

Here are five related questions:

1. What are supplementary angles, and how do they differ from complementary angles?
2. Can two obtuse angles ever be complementary?
3. How can you verify if two angles are complementary in a more complex diagram?
4. What are adjacent angles, and how do they differ from vertical angles?
5. Are complementary angles always acute?

Tip: Complementary angles always add up to 90 degrees, regardless of their individual sizes, but they must both be acute since obtuse angles cannot complement each other.