Question

select all the pairs of alternate exterior angles.

∠lki and ∠mnp
∠lki and ∠onk
∠mnp and ∠onk
∠mnk and ∠onk

Explanation:

Step1: Recall alternate - exterior angles definition

Alternate - exterior angles are two non - adjacent exterior angles on opposite sides of a transversal.

Step2: Analyze the given angles

For the lines and transversal in the figure, we check each pair.

• $\angle LKI$ and $\angle MNP$: They are non - adjacent exterior angles on opposite sides of the transversal, so they are alternate - exterior angles.
• $\angle LKI$ and $\angle ONK$: They are non - adjacent exterior angles on opposite sides of the transversal, so they are alternate - exterior angles.
• $\angle MNP$ and $\angle ONK$: They are non - adjacent exterior angles on opposite sides of the transversal, so they are alternate - exterior angles.
• $\angle MNK$ and $\angle ONK$ are not alternate - exterior angles as $\angle MNK$ is an interior angle.

Answer:

$\angle LKI$ and $\angle MNP$, $\angle LKI$ and $\angle ONK$, $\angle MNP$ and $\angle ONK$