Question

select all the pairs of alternate exterior angles.
∠fgj and ∠kjl ∠kjl and ∠fge
∠hge and ∠ijl ∠fge and ∠ijl

Explanation:

Step1: Recall Alternate Exterior Angles Definition

Alternate exterior angles are formed when a transversal crosses two parallel lines. They lie outside the two lines and on opposite sides of the transversal.

Step2: Analyze Each Pair

• For $\angle F G J$ and $\angle K J L$: $\angle F G J$ is outside the two vertical lines (IF and KH) and on one side of transversal LE, $\angle K J L$ is outside the two vertical lines and on the opposite side of transversal LE. So they are alternate exterior angles.
• For $\angle K J L$ and $\angle F G E$: $\angle K J L$ is outside, $\angle F G E$ is inside the two vertical lines, so not alternate exterior.
• For $\angle H G E$ and $\angle I J L$: $\angle H G E$ is outside, $\angle I J L$ is outside and on opposite sides of transversal LE. So they are alternate exterior angles.
• For $\angle F G E$ and $\angle I J L$: $\angle F G E$ is inside, $\angle I J L$ is outside, so not alternate exterior.

Answer:

$\angle F G J$ and $\angle K J L$, $\angle H G E$ and $\angle I J L$