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.
What is the relationship between angle 6 and angle 7?(1 point)
Responses
vertical angles
corresponding angles
alternate exterior angles
alternate interior angles
The relationship between angle 6 and angle 7 is that they are corresponding angles.
The relationship between angle 6 and angle 7 is "corresponding angles".
To determine the relationship between angle 6 and angle 7, we need to recall some geometric angle relationships. In this case, the inclined transversal intersects two vertical lines (M and N), which means we can use certain angle relationships to find the answer.
1. Vertical angles: When two lines intersect, the opposite angles formed are called vertical angles. Vertical angles are congruent, meaning they have the same measure. However, from the given information, we are not directly dealing with vertical angles.
2. Corresponding angles: Corresponding angles are formed when a transversal intersects two parallel lines. These angles are in corresponding positions, meaning they occupy the same relative positions at each intersection point. Corresponding angles are also congruent. However, angle 6 and angle 7 are not in corresponding positions, so we can eliminate corresponding angles as the answer.
3. Alternate exterior angles: Alternate exterior angles are formed when a transversal intersects two parallel lines, and they lie on the opposite sides of the transversal. Alternate exterior angles are congruent. From the provided information, we are not dealing with alternate exterior angles.
4. Alternate interior angles: Alternate interior angles are formed when a transversal intersects two parallel lines, and they lie on the opposite sides of the transversal but between the parallel lines. These angles are congruent. In this case, angle 6 and angle 7 are alternate interior angles since they are on opposite sides of the transversal (labeled M and N) and between the parallel lines. Therefore, the correct answer is "alternate interior angles."
In summary, the relationship between angle 6 and angle 7 is that they are alternate interior angles.