Question

identify four statements that prove line a is parallel to line b.
∠1≅∠5
∠2≅∠7
∠3≅∠6
∠5≅∠8
m∠1 + m∠2 = 180
m∠4 + m∠6 = 180

Explanation:

Step1: Recall parallel - line postulates

If corresponding angles are congruent, lines are parallel. ∠1 and ∠5 are corresponding angles. If ∠1≅∠5, then line a is parallel to line b.

Step2: Consider alternate - interior angles

If alternate - interior angles are congruent, lines are parallel. ∠3 and ∠6 are alternate - interior angles. If ∠3≅∠6, then line a is parallel to line b.

Step3: Look at alternate - exterior angles

If alternate - exterior angles are congruent, lines are parallel. ∠2 and ∠7 are alternate - exterior angles. If ∠2≅∠7, then line a is parallel to line b.

Step4: Analyze same - side interior angles

If same - side interior angles are supplementary, lines are parallel. ∠4 and ∠6 are same - side interior angles. If m∠4 + m∠6=180, then line a is parallel to line b.

Answer:

∠1≅∠5, ∠3≅∠6, ∠2≅∠7, m∠4 + m∠6 = 180