In the given diagram, we are looking for supplementary angles. Supplementary angles are two angles that add up to 180 degrees.

From the diagram, several pairs of angles are formed by intersecting lines. Typically, adjacent angles on a straight line (linear pairs) are supplementary because they sum to 180 degrees.

Let's examine the pairs of angles based on the choices provided:

1. ∠GHJ and ∠DEH: These are not adjacent, and they don’t form a linear pair, so they are not supplementary.
2. ∠DEC and ∠GHE: These angles also do not form a linear pair, so they are not supplementary.
3. ∠DEC and ∠FEH: These angles look like a linear pair because ∠DEC and ∠FEH are adjacent and form a straight line at point E. Therefore, they are supplementary.
4. ∠DEC and ∠FEC: These angles are on the same side of the line but do not form a linear pair, so they are not supplementary.

The correct answer is ∠DEC and ∠FEH.

Would you like a further explanation of this concept, or have any other questions?

Here are some related questions:

1. What are linear pairs of angles?
2. Can vertically opposite angles be supplementary?
3. How do you find complementary angles?
4. What is the sum of adjacent angles on a straight line?
5. How can we determine if two angles are supplementary based on their measures?

Tip: Always look for linear pairs when identifying supplementary angles in intersecting lines.