Supplementary Angles Ee5E31

1. **Problem Statement:** Identify which pairs of angles are supplementary angles. 2. **Definition:** Supplementary angles are two angles whose measures add up to $$180^\circ$$. 3. **Given Angles:** - $$\angle IJL$$ is formed at point $$J$$ between points $$I$$ and $$L$$. - $$\angle HGE$$ is formed at point $$G$$ between points $$H$$ and $$E$$. - $$\angle FGJ$$ is formed at point $$G$$ between points $$F$$ and $$J$$. - $$\angle KJG$$ is formed at point $$J$$ between points $$K$$ and $$G$$. - $$\angle IJG$$ is formed at point $$J$$ between points $$I$$ and $$G$$. 4. **Analyze pairs:** - $$\angle IJL$$ and $$\angle HGE$$: These angles are at different points ($$J$$ and $$G$$) and not adjacent or forming a straight line, so unlikely supplementary. - $$\angle IJL$$ and $$\angle FGJ$$: $$\angle IJL$$ is at $$J$$, $$\angle FGJ$$ is at $$G$$; these points are connected by the slanted line but angles are not adjacent or forming a straight line. - $$\angle IJL$$ and $$\angle KJG$$: Both angles share vertex $$J$$. - $$\angle IJL$$ is between $$I$$ and $$L$$. - $$\angle KJG$$ is between $$K$$ and $$G$$. - Since $$I-J-K$$ is a straight horizontal line and $$L-J-G$$ is the slanted line, $$\angle IJL$$ and $$\angle KJG$$ are adjacent angles on a straight line. - Therefore, $$\angle IJL + \angle KJG = 180^\circ$$, so they are supplementary. - $$\angle IJL$$ and $$\angle IJG$$: Both share vertex $$J$$ and points $$I$$ and $$J$$, but $$\angle IJG$$ is between $$I$$ and $$G$$, which is part of the slanted line. - These two angles overlap and do not form a linear pair. 5. **Conclusion:** The supplementary angles are $$\angle IJL$$ and $$\angle KJG$$. **Final answer:** $$\boxed{\angle IJL \text{ and } \angle KJG \text{ are supplementary angles}}$$.