Question

select all the pairs of consecutive interior angles.

Explanation:

Step1: Recall definition of consecutive - interior angles

Consecutive - interior angles are two angles that lie between two lines and on the same side of a transversal.

Step2: Analyze each pair

• For $\angle{FGJ}$ and $\angle{IJG}$: They lie between lines $FH$ and $IK$ and on the same side of transversal $IL$, so they are consecutive - interior angles.
• For $\angle{HGE}$ and $\angle{HGJ}$: They are adjacent angles, not consecutive - interior angles.
• For $\angle{HGJ}$ and $\angle{KJG}$: They lie between lines $FH$ and $IK$ and on the same side of transversal $IL$, so they are consecutive - interior angles.
• For $\angle{HGJ}$ and $\angle{KJL}$: $\angle{KJL}$ is not in the correct position relative to $\angle{HGJ}$ to be a consecutive - interior angle.

Answer:

$\angle{FGJ}$ and $\angle{IJG}$, $\angle{HGJ}$ and $\angle{KJG}$