Question

lines l and m are parallel lines. select all of the angles that are congruent to ∠2.

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are congruent. $\angle2$ and $\angle4$ are vertical angles, so $\angle2\cong\angle4$.

Step2: Identify corresponding - angle relationship

Corresponding angles formed by parallel lines are congruent. $\angle2$ and $\angle6$ are corresponding angles, so $\angle2\cong\angle6$.

Step3: Identify alternate - exterior - angle relationship

Alternate - exterior angles formed by parallel lines are congruent. $\angle2$ and $\angle8$ are alternate - exterior angles, so $\angle2\cong\angle8$.

Answer:

$\angle4$, $\angle6$, $\angle8$