Question

in the figure, the angles are formed by a transversal and two parallel lines. which angles seem to be congruent?
○ ∠1 @ ∠4 @ ∠5 @ ∠8;
∠2 @ ∠3 @ ∠6 @ ∠7
○ ∠1 @ ∠2 @ ∠5 @ ∠6;
∠3 @ ∠4 @ ∠7 @ ∠8
○ ∠1 @ ∠2 @ ∠3 @ ∠4;
∠5 @ ∠6 @ ∠7 @ ∠8
○ ∠1 @ ∠3 @ ∠5 @ ∠7;
∠2 @ ∠4 @ ∠6 @ ∠8

Explanation:

Step1: Recall angle - pair relationships

When a transversal intersects two parallel lines, vertical angles are congruent. ∠1 and ∠4, ∠2 and ∠3, ∠5 and ∠8, ∠6 and ∠7 are vertical - angle pairs.

Step2: Recall corresponding angles

Corresponding angles are congruent. ∠1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, ∠4 and ∠8 are corresponding - angle pairs.

Step3: Recall alternate - interior and alternate - exterior angles

Alternate - interior angles are congruent (∠3 and ∠5, ∠2 and ∠8) and alternate - exterior angles are congruent (∠1 and ∠7, ∠4 and ∠6). Combining these facts, we get ∠1 ≅ ∠4 ≅ ∠5 ≅ ∠8 and ∠2 ≅ ∠3 ≅ ∠6 ≅ ∠7.

Answer:

A. ∠1 ≅ ∠4 ≅ ∠5 ≅ ∠8; ∠2 ≅ ∠3 ≅ ∠6 ≅ ∠7