Question

the figure shows a pair of parallel lines cut by a transversal. which three angles are congruent to ∠2? choose all three correct angles. ∠3 ∠4 ∠5 ∠6 ∠7 ∠8

Explanation:

Step1: Vertical angles

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

Step2: Corresponding angles

When two parallel lines are cut by a transversal, corresponding angles are congruent. $\angle2$ and $\angle6$ are corresponding angles. So $\angle2\cong\angle6$.

Step3: Alternate - exterior angles

When two parallel lines are cut by a transversal, alternate - exterior angles are congruent. $\angle2$ and $\angle8$ are alternate - exterior angles. So $\angle2\cong\angle8$.

Answer:

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