Question

which angles are supplementary angles?
∠kjg and ∠ijl ∠fge and ∠hge
∠hge and ∠fgj ∠fge and ∠kjl
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not feeling ready yet? these can help:
identify complementary, supplementary, vertical, adjace.. (0)
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lesson: transversals of parallel lines
lesson: adjacent angles
lesson: vertical angles

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles are two angles whose sum is $180^{\circ}$.

Step2: Analyze each pair of angles

• For $\angle KJG$ and $\angle IJL$: These are vertical angles (equal in measure), not supplementary.
• For $\angle FGE$ and $\angle HGE$: They form a linear - pair (adjacent angles on a straight line). By the linear - pair postulate, $\angle FGE+\angle HGE = 180^{\circ}$.
• For $\angle HGE$ and $\angle FGJ$: There is no relation that makes their sum $180^{\circ}$.
• For $\angle FGE$ and $\angle KJL$: There is no relation that makes their sum $180^{\circ}$.

Answer:

$\angle FGE$ and $\angle HGE$