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

corresponding angles
corresponding angles

alternate interior angles
alternate interior angles

vertical angles
vertical angles

alternate exterior angles
alternate exterior angles
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1 answer

To analyze the relationship between angle 6 and angle 7 based on their positions relative to the transversal and the parallel lines M and N, we can use the definitions of the different angle relationships.

  1. Corresponding Angles: These are angles that occupy the same relative position at each intersection. Angle 6 and angle 7 are not in corresponding positions since they are on different parallel lines.

  2. Alternate Interior Angles: These angles lie between the two parallel lines and on opposite sides of the transversal. Angle 6 is on one side of the transversal and angle 7 is on the opposite side of the transversal but between the two parallels. Thus, they form an alternate interior angles relationship.

  3. Vertical Angles: These angles are opposite each other when two lines cross. Angles 6 and 7 are not vertical angles since they do not occupy that position.

  4. Alternate Exterior Angles: These angles lie outside the two parallel lines and on opposite sides of the transversal. Angle 6 is inside the parallel lines while angle 7 is also inside, hence they are not alternate exterior angles.

Based on these definitions, the relationship between angle 6 and angle 7 is best described as:

alternate interior angles.

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