Question

angle pair relationships
write the angle relationship for each pair of angles.

1. (angle j) and (angle f) are
2. (angle e) and (angle g) are
3. (angle j) and (angle k) are
4. (angle g) and (angle i) are
5. (angle h) and (angle l) are
6. (angle k) and (angle e) are
7. (angle f) and (angle k) are
8. (angle h) and (angle g) are
9. (angle e) and (angle h) are

Explanation:

Step1: Recall angle - pair relationships

• Corresponding angles: Angles in the same relative position.
• Vertical angles: Opposite angles formed by two intersecting lines.
• Alternate interior angles: Angles between two parallel lines and on opposite sides of a transversal.
• Alternate exterior angles: Angles outside two parallel lines and on opposite sides of a transversal.
• Consecutive interior angles (same - side interior angles): Angles between two parallel lines and on the same side of a transversal.

Step2: Analyze each pair

1. For \(\angle J\) and \(\angle F\)

• They are in the same relative position. So, \(\angle J\) and \(\angle F\) are corresponding angles.

1. For \(\angle E\) and \(\angle G\)

• They are opposite angles formed by two intersecting lines. So, \(\angle E\) and \(\angle G\) are vertical angles.

1. For \(\angle J\) and \(\angle K\)

• They are opposite angles formed by two intersecting lines. So, \(\angle J\) and \(\angle K\) are vertical angles.

1. For \(\angle G\) and \(\angle I\)

• They are between two parallel lines and on opposite sides of a transversal. So, \(\angle G\) and \(\angle I\) are alternate interior angles.

1. For \(\angle H\) and \(\angle L\)

• They are in the same relative position. So, \(\angle H\) and \(\angle L\) are corresponding angles.

1. For \(\angle K\) and \(\angle E\)

• They are outside two parallel lines and on opposite sides of a transversal. So, \(\angle K\) and \(\angle E\) are alternate exterior angles.

1. For \(\angle F\) and \(\angle K\)

• They are between two parallel lines and on the same side of a transversal. So, \(\angle F\) and \(\angle K\) are consecutive interior angles.

1. For \(\angle H\) and \(\angle G\)

• They form a linear pair (sum to \(180^{\circ}\)). So, \(\angle H\) and \(\angle G\) are supplementary angles (adjacent supplementary angles).

1. For \(\angle E\) and \(\angle H\)

• They form a linear pair (sum to \(180^{\circ}\)). So, \(\angle E\) and \(\angle H\) are supplementary angles (adjacent supplementary angles).

Answer:

1. Corresponding angles
2. Vertical angles
3. Vertical angles
4. Alternate interior angles
5. Corresponding angles
6. Alternate exterior angles
7. Consecutive interior angles
8. Supplementary angles (adjacent supplementary angles)
9. Supplementary angles (adjacent supplementary angles)