Question

1. given lines l and m are parallel, match the angle pair to the correct term:
2. ∠4 and ∠6
3. ∠1 and ∠2
4. ∠1 and ∠7
5. ∠3 and ∠6
6. ∠5 and ∠7
7. ∠1 and ∠5

a. alternate exterior angles
b. alternate interior angles
c. vertical angles
d. linear pair
e. corresponding angles
f. consecutive interior angles

Explanation:

Step1: Recall angle - pair definitions

• Alternate interior angles: Two non - adjacent interior angles on opposite sides of the transversal.
• Linear pair: Two adjacent angles that form a straight line (\(\angle1+\angle2 = 180^{\circ}\) as they are adjacent and their non - common sides form a straight line).
• Alternate exterior angles: Two non - adjacent exterior angles on opposite sides of the transversal. \(\angle1\) is an exterior angle and \(\angle7\) is also an exterior angle, and they are on opposite sides of the transversal.
• Consecutive interior angles: Two interior angles on the same side of the transversal.
• Vertical angles: Opposite angles formed by the intersection of two lines.
• Corresponding angles: Angles in the same relative position with respect to the parallel lines and the transversal.

Step2: Match each angle pair

1. For \(\angle4\) and \(\angle6\):

• They are non - adjacent interior angles on opposite sides of the transversal. So, \(\angle4\) and \(\angle6\) are alternate interior angles (b).

1. For \(\angle1\) and \(\angle2\):

• They are adjacent angles and \(\angle1+\angle2=180^{\circ}\) (since they form a straight line). So, \(\angle1\) and \(\angle2\) are a linear pair (d).

1. For \(\angle1\) and \(\angle7\):

• \(\angle1\) is an exterior angle and \(\angle7\) is an exterior angle, and they are on opposite sides of the transversal. So, \(\angle1\) and \(\angle7\) are alternate exterior angles (a).

1. For \(\angle3\) and \(\angle6\):

• They are interior angles on the same side of the transversal. So, \(\angle3\) and \(\angle6\) are consecutive interior angles (f).

1. For \(\angle5\) and \(\angle7\):

• They are opposite angles formed by the intersection of two lines. So, \(\angle5\) and \(\angle7\) are vertical angles (c).

1. For \(\angle1\) and \(\angle5\):

• \(\angle1\) and \(\angle5\) are in the same relative position with respect to the parallel lines and the transversal. So, \(\angle1\) and \(\angle5\) are corresponding angles (e).

Answer:

1. b. alternate interior angles
2. d. linear pair
3. a. alternate exterior angles
4. f. consecutive interior angles
5. c. vertical angles
6. e. corresponding angles