Question

which angles are congruent to ∠6? choose all that apply. ∠1 ∠2 ∠3 ∠4 ∠5 ∠7 ∠8

Explanation:

Step1: Vertical angles

Vertical angles are congruent. $\angle2$ and $\angle4$ are vertical angles. But this is not directly relevant here.

Step2: Corresponding angles

$\angle6$ and $\angle2$ are corresponding angles. When two parallel lines are cut by a transversal (assuming the lines are parallel as per angle - relationship context), corresponding angles are congruent.

Step3: Alternate - interior angles

$\angle6$ and $\angle4$ are alternate - interior angles. Alternate - interior angles are congruent when lines are parallel.

Step4: Alternate - exterior angles

$\angle6$ has no alternate - exterior angles in this basic intersection shown. But considering the vertical - angle relationship of the angles formed by the intersection: $\angle2\cong\angle4$ (vertical angles), and since $\angle6\cong\angle2$ (corresponding) and $\angle6\cong\angle4$ (alternate - interior), and also $\angle6$ and $\angle8$: $\angle4\cong\angle8$ (corresponding if we extend the parallel - line logic for the transversal - like intersection), and since $\angle6\cong\angle4$, then $\angle6\cong\angle8$.

Answer:

$\angle2$, $\angle4$, $\angle8$