Using facts about the angles formed when parallel lines are cut by a transversal, what relationship can you establish between angle 5 and angle 1?

Question

Responses

alternate interior angles
alternate interior angles - no response given

vertical angles
vertical angles - no response given

corresponding angles
corresponding angles - not selected, this is the correct answer

alternate exterior angles

please show work

Answer 1

To establish the relationship between angle 5 and angle 1, we need to know the angle relationships formed when parallel lines are cut by a transversal.

When parallel lines are cut by a transversal, the following angle relationships are formed:

1. Alternate interior angles: These angles are located on opposite sides of the transversal and inside the two parallel lines. They are congruent (have the same measure). In this case, angle 5 and angle 1 are not alternate interior angles because they are not located on opposite sides of the transversal.

2. Vertical angles: These angles are formed by the intersection of two lines and are opposite each other. They are always congruent. Since angle 5 and angle 1 are not opposite each other, they are not vertical angles.

3. Corresponding angles: These angles are in the same position relative to the transversal. They are congruent. In this case, angle 5 and angle 1 are corresponding angles because they are in the same position relative to the transversal.

4. Alternate exterior angles: These angles are located on opposite sides of the transversal and outside the two parallel lines. They are congruent. Angle 5 and angle 1 are not alternate exterior angles because they are not located on opposite sides of the transversal.

Therefore, the correct relationship established between angle 5 and angle 1 is that they are corresponding angles.