In the provided image, we have several intersecting lines forming angles, and the question seems to ask for a pair of angles that have a specific relationship—most likely either vertical angles, corresponding angles, or adjacent angles.

Let's review the possible angle pair relationships:

1. Vertical angles: These are opposite each other when two lines intersect. They are always congruent.
2. Corresponding angles: These appear in the same relative position when a transversal crosses parallel lines. They are also congruent if the lines are parallel.
3. Adjacent angles: These share a common arm and vertex, but do not overlap. Their sum equals 180° if they form a straight line.

Let’s go through the options:

1. ∠FEH and ∠FEC:

   • These angles appear adjacent. ∠FEH and ∠FEC share the arm EF, and together they form a straight line (EH and EC). Thus, they are supplementary adjacent angles.

2. ∠DEH and ∠GHJ:

   • These are vertical angles. Since the two lines DG and IJ intersect at point H, these two angles are directly opposite each other and are therefore congruent.

3. ∠DEH and ∠FEC:

   • These angles are not directly related by vertical, corresponding, or adjacent angle rules.

4. ∠IHJ and ∠FEC:

   • These angles also do not have a direct relationship that we can identify based on the geometry of the diagram.

Correct Answer:

• Option 2: ∠DEH and ∠GHJ are vertical angles and hence congruent.

Would you like more details on any specific relationships between the angles or further clarifications?

Here are some additional related questions for you:

1. What are the properties of vertical angles?
2. Can adjacent angles ever be congruent? If so, under what conditions?
3. How do we determine if lines are parallel based on angles?
4. What is the sum of adjacent supplementary angles?
5. How are corresponding angles used to identify parallel lines?

Tip: Vertical angles are always equal, making them a helpful tool in geometric proofs.