1. **Problem Statement:** Given two parallel lines $\overrightarrow{FH}$ and $\overrightarrow{IK}$ intersected by a transversal $\overrightarrow{EL}$ passing through points $G$ and $J$, identify which pairs of angles are alternate interior angles. 2. **Key Concept:** Alternate interior angles are pairs of angles that lie between the two parallel lines on opposite sides of the transversal. They are congruent (equal in measure). 3. **Analyze the angles:** - $\angle KJG$ is at point $J$ on the lower line $\overrightarrow{IK}$. - $\angle FGJ$ is at point $G$ on the upper line $\overrightarrow{FH}$. - $\angle KJL$ is at point $J$ on the lower line. - $\angle IJG$ is at point $J$ on the lower line. - $\angle HGE$ is at point $G$ on the upper line. 4. **Check pairs:** - $\angle KJG$ and $\angle FGJ$: $KJG$ is on the lower line, $FGJ$ is on the upper line, and they are on opposite sides of the transversal $\overrightarrow{EL}$. This fits the definition of alternate interior angles. - $\angle KJG$ and $\angle KJL$: Both angles are at point $J$ on the lower line, so they cannot be alternate interior angles. - $\angle KJG$ and $\angle IJG$: Both angles are on the lower line, so not alternate interior. - $\angle KJG$ and $\angle HGE$: $KJG$ is on the lower line, $HGE$ is on the upper line, but both are on the same side of the transversal, so not alternate interior. 5. **Conclusion:** The pair of alternate interior angles is $\angle KJG$ and $\angle FGJ$. **Final answer:** $\angle KJG$ and $\angle FGJ$ are alternate interior angles.