An inclined transversal passes through two vertical parallel lines labeled upper M and upper N. The angles formed around the intersection point of upper M are labeled clockwise, starting from the upper left quadrant: 1, 2, 4, and 3. The corresponding angles formed around the intersection point of upper N are labeled clockwise, starting from the upper left quadrant: 5, 6, 8, and 7.
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?
alternate interior angles
vertical angles
alternate exterior angles
corresponding angles
The relationship that can be established between angle 5 and angle 1 is alternate exterior angles.
Alternate exterior angles are formed when a transversal intersects two parallel lines and are located on opposite sides of the transversal and outside the two parallel lines. In this case, angle 5 and angle 1 are alternate exterior angles because they are located on opposite sides of the transversal (the inclined transversal passing through upper M) and outside the two parallel lines (upper M and upper N).
The relationship that can be established between angle 5 and angle 1, based on the facts about the angles formed when parallel lines are cut by a transversal, is that they are corresponding angles.
To determine the relationship between angle 5 and angle 1, we can use the properties of angles formed when parallel lines are cut by a transversal.
The property that applies in this case is called "corresponding angles." Corresponding angles are angles that are in the same relative position at each intersection point where the transversal cuts the parallel lines.
In the given scenario, angle 1 at the intersection of line M corresponds to angle 5 at the intersection of line N. This means that angle 1 and angle 5 are corresponding angles.
Therefore, the relationship that can be established between angle 5 and angle 1 is that they are corresponding angles.