Question

which angles are congruent to each other? ∠4 and ∠2 ∠1 and ∠2 ∠2 and ∠8 ∠6 and ∠2

Explanation:

Step1: Recall vertical - angle property

Vertical angles are congruent. ∠1 and ∠3, ∠2 and ∠4, ∠5 and ∠7, ∠6 and ∠8 are vertical angles.

Step2: Recall corresponding - angle property

If two parallel lines are cut by a transversal, corresponding angles are congruent. ∠2 and ∠6, ∠4 and ∠8, ∠1 and ∠5, ∠3 and ∠7 are corresponding angles.

Step3: Recall alternate - interior and alternate - exterior angle properties

Alternate - interior angles are congruent (∠1 and ∠7, ∠4 and ∠6) and alternate - exterior angles are congruent (∠2 and ∠8, ∠3 and ∠5).

Answer:

∠2 and ∠8