Question

1c. classify the relationship between each pair of angles as alternate interior, alternate exterior, corresponding consecutive interior, linear or vertical.
1 and 4:__________
1 and 8:__________
6 and 4:__________
3 and 6:__________
2 and 6:__________
7 and 8:__________

Explanation:

Step1: Recall angle - pair relationships

Vertical angles are opposite each other when two lines intersect.

Step2: Analyze ∠1 and ∠4

∠1 and ∠4 are opposite each other at the intersection of lines \(b\) and \(c\), so they are vertical angles.

Step3: Analyze ∠1 and ∠8

∠1 and ∠8 are on the outside of the two lines \(a\) and \(c\) and on opposite sides of the transversal \(b\), so they are alternate - exterior angles.

Step4: Analyze ∠6 and ∠4

∠6 and ∠4 are on the inside of the two lines \(a\) and \(c\) and on opposite sides of the transversal \(b\), so they are alternate - interior angles.

Step5: Analyze ∠3 and ∠6

∠3 and ∠6 are on the inside of the two lines \(a\) and \(c\) and on the same side of the transversal \(b\), so they are consecutive - interior angles.

Step6: Analyze ∠2 and ∠6

∠2 and ∠6 are in the same relative position with respect to the intersection of lines \(b\) and \(c\) and the intersection of lines \(a\) and \(b\), so they are corresponding angles.

Step7: Analyze ∠7 and ∠8

∠7 and ∠8 are adjacent and form a straight - line, so they are linear pair.

Answer:

1 and 4: vertical
1 and 8: alternate exterior
6 and 4: alternate interior
3 and 6: consecutive interior
2 and 6: corresponding
7 and 8: linear