Question

use the diagram below to classify each pair of angles.

answer
angle 6 and angle 8:
angle 1 and angle 8:
angle 6 and angle 7:
angle 2 and angle 7:
angle 1 and angle 4:

Explanation:

Step1: Recall angle - pair definitions

• Vertical angles: Angles opposite each other when two lines intersect.
• Corresponding angles: Angles in the same relative position.
• 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: Angles between two parallel lines and on the same side of a transversal.

Step2: Classify Angle 6 and Angle 8

• Angle 6 and Angle 8 are not in the same relative position (not corresponding), not between the parallel lines (not alternate interior), not outside the parallel lines (not alternate exterior), not on the same side of the transversal (not consecutive interior). They are vertical angles (opposite each other at the intersection of two lines).

Step3: Classify Angle 1 and Angle 8

• Angle 1 and Angle 8 are not vertical (not opposite at the same intersection). They are not between the parallel lines (not alternate interior). They are not in the same relative position (not corresponding). They are alternate exterior angles (outside the parallel lines and on opposite sides of the transversal).

Step4: Classify Angle 6 and Angle 7

• Angle 6 and Angle 7 are not vertical (not opposite at the same intersection). They are not alternate exterior (not outside the parallel lines). They are not corresponding (not in the same relative position). They are consecutive interior angles (between the parallel lines and on the same side of the transversal).

Step5: Classify Angle 2 and Angle 7

• Angle 2 and Angle 7 are not vertical (not opposite at the same intersection). They are not consecutive interior (not on the same side of the transversal). They are not corresponding (not in the same relative position). They are alternate interior angles (between the parallel lines and on opposite sides of the transversal).

Step6: Classify Angle 1 and Angle 4

• Angle 1 and Angle 4 are not vertical (not opposite at the same intersection). They are not alternate interior (not between the parallel lines). They are not consecutive interior (not between the parallel lines). They are not corresponding (not in the same relative position). They are alternate exterior angles (outside the parallel lines and on opposite sides of the transversal).

Answer:

Angle 6 and Angle 8: Vertical angles
Angle 1 and Angle 8: Alternate exterior angles
Angle 6 and Angle 7: Consecutive interior angles
Angle 2 and Angle 7: Alternate interior angles
Angle 1 and Angle 4: Alternate exterior angles