Question

which of the following options is a pair of alternate exterior angles? ∠5 and ∠10 ∠1 and ∠8 ∠1 and ∠9 ∠1 and ∠10

Explanation:

Step1: Recall alternate - exterior angles definition

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

Step2: Analyze each option

For $\angle5$ and $\angle10$, they are not on the opposite sides of the transversal, so they are not alternate - exterior angles.
For $\angle1$ and $\angle8$, $\angle1$ is an exterior angle and $\angle8$ is an interior angle, so they are not alternate - exterior angles.
For $\angle1$ and $\angle9$, $\angle1$ and $\angle9$ are non - adjacent exterior angles and lie on the opposite sides of the transversal.
For $\angle1$ and $\angle10$, $\angle10$ is an interior angle, so they are not alternate - exterior angles.

Answer:

$\angle1$ and $\angle9$