Question

check your understanding
use the picture on the right for questions 1 - 3. lines l and m are parallel.

1. what is the relationship between angles 3 and 6?
2. which pairs of angles are supplementary?

Explanation:

Step1: Recall angle - pair relationships

When two parallel lines are cut by a transversal, angles 3 and 6 are alternate - interior angles.

Step2: Identify supplementary angle pairs

Supplementary angles add up to 180 degrees. For parallel lines \(l\) and \(m\) cut by transversal \(t\), linear - pair angles and same - side interior angles are supplementary. Linear - pair angles: \((\angle1,\angle2),(\angle3,\angle4),(\angle5,\angle6),(\angle7,\angle8)\); Same - side interior angles: \((\angle3,\angle5),(\angle4,\angle6)\)

Answer:

1. Angles 3 and 6 are alternate - interior angles.
2. Supplementary angle pairs are \((\angle1,\angle2),(\angle3,\angle4),(\angle5,\angle6),(\angle7,\angle8),(\angle3,\angle5),(\angle4,\angle6)\)