The question is asking which pairs of angles are supplementary. In geometry, supplementary angles are two angles whose sum is $180^\circ$.

From the image, the key points to consider are the straight lines, as supplementary angles are often adjacent angles formed when a straight line is crossed by another line. Let's analyze the diagram:

• $\angle HGJ$ and $\angle IJG$: These two angles appear to be adjacent on a straight line, sharing point $J$, making them supplementary.
• $\angle HGJ$ and $\angle FGE$: These angles are not adjacent and do not form a linear pair, so they are not supplementary.
• $\angle HGJ$ and $\angle HGE$: These angles are on the same straight line, sharing point $G$, which means they add up to $180^\circ$ and are supplementary.
• $\angle HGJ$ and $\angle KJL$: These angles are not adjacent or on the same straight line, so they are not supplementary.

Therefore, the correct answer should be $\angle HGJ$ and $\angle HGE$.

Would you like a detailed explanation of supplementary angles?

Here are 5 questions related to this topic:

1. What is the difference between supplementary and complementary angles?
2. How can you identify vertical angles in this diagram?
3. Can angles on parallel lines be supplementary?
4. What are linear pairs of angles, and how do they relate to supplementary angles?
5. How are alternate interior angles formed when a transversal crosses two lines?

Tip: Always look for straight lines when identifying supplementary angles, as they often form adjacent angle pairs adding up to 180 degrees.