Angles and parallel lines quick check use the figure to answer the questions mn1234-5678 using the facts about the angles formed when parallel lines are cut by a transversal what relationship can be established between angle 5 and angle 1 alternate exterior angles vertical angles alterior and then interior angles corresponding angles
Based on the given figure, angle 5 and angle 1 are corresponding angles.
The relationships that can be established between these angles are:
1. Corresponding angles: When a transversal intersects two parallel lines, the corresponding angles formed on the same side of the transversal and in the same position are congruent. Therefore, angle 5 and angle 1 are congruent.
2. Alternate exterior angles: When a transversal intersects two parallel lines, the alternate exterior angles formed on opposite sides of the transversal and outside the parallel lines are congruent. In the given figure, angle 5 is an exterior angle on the left side of the transversal, and angle 1 is an exterior angle on the right side of the transversal. They are alternate exterior angles, but their relationship cannot be established as congruent in this case.
3. Vertical angles: Vertical angles are formed by the intersection of two lines and are congruent. In the given figure, angles 5 and 1 are not vertical angles as they are not formed by the intersection of two lines.
4. Interior angles: Interior angles are angles formed on the same side of the transversal and between the parallel lines. In the given figure, angle 5 and angle 1 are not interior angles as they are not on the same side of the transversal and between the parallel lines.
Therefore, based on the figure and the facts about angles formed when parallel lines are cut by a transversal, the established relationship between angle 5 and angle 1 is that they are corresponding angles and are congruent.