Question

∠2 and ​​​​are alternate exterior angles.

a. ∠9
b. ∠10
c. ∠13
d. ∠14

Explanation:

Step1: Recall the definition of alternate exterior angles

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

Step2: Identify the transversal and the lines

Here, line \(m\) and line \(l\) are cut by transversal \(k\).
For \(\angle2\), we check each option:

• \(\angle9\): It is not an alternate exterior angle with \(\angle2\) as they are not on the opposite sides of the transversal in the correct exterior - non - adjacent position.
• \(\angle10\): \(\angle2\) and \(\angle10\) are non - adjacent, exterior (relative to the parallel lines \(m\) and \(l\)) and lie on opposite sides of the transversal \(k\).
• \(\angle13\): It is not in the correct position relative to \(\angle2\) to be an alternate exterior angle.
• \(\angle14\): It is not in the correct position relative to \(\angle2\) to be an alternate exterior angle.

Answer:

B. \(\angle10\)