Question

Question

Use the figure to answer the question.

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

alternate interior angles
alternate interior angles

corresponding angles
corresponding angles

alternate exterior angles
alternate exterior angles

vertical angles

Answer 1

To determine the relationship between angle 6 and angle 7, we can analyze their positions in relation to the two parallel lines (M and N) and the transversal.

• Angle 6 is on the upper part of line N, while angle 7 is on the lower part of line N.
• Angles 6 and 7 are inside the parallel lines (M and N).

According to the properties of angles formed by a transversal and parallel lines:

• Corresponding angles are on the same side of the transversal and are in corresponding positions relative to the parallel lines.
• Alternate interior angles are on opposite sides of the transversal and inside the parallel lines.

Since angle 6 and angle 7 are on opposite sides of the transversal and inside the parallel lines, they are considered alternate interior angles.

Therefore, the correct answer is:

alternate interior angles

Answer 2

Use the figure to answer the question.

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 3 and angle 6?

(1 point)
Responses

alternate interior angles
alternate interior angles

alternate exterior angles
alternate exterior angles

vertical angles
vertical angles

corresponding angles

Answer 3

To determine the relationship between angle 3 and angle 6, we need to analyze their positions relative to the two parallel lines (M and N) and the transversal.

1. Angle 3 is located at the intersection of line M and the transversal, specifically in the bottom right quadrant.
2. Angle 6 is located at the intersection of line N and the transversal, specifically in the upper right quadrant.

Now, we can assess the types of angles they are:

• Corresponding angles are located in the same relative position at the two intersections formed by the transversal and the parallel lines.
• Alternate interior angles are located on opposite sides of the transversal and between the two parallel lines.
• Vertical angles are opposite angles formed by two intersecting lines.

In this case, angle 3 and angle 6 are on the same side of the transversal and are in the corresponding position relative to the parallel lines, which makes them corresponding angles.

Therefore, the correct answer is:

corresponding angles