Question

7)
a) same - side interior
b) alternate interior
c) alternate exterior
d) corresponding

Explanation:

To determine the angle relationship between \( x \) and \( y \):

1. Recall the definitions of angle pairs formed by parallel lines and a transversal:

• Same - side interior angles: Lie on the same side of the transversal and between the two lines.
• Alternate interior angles: Lie between the two lines and on opposite sides of the transversal.
• Alternate exterior angles: Lie outside the two lines and on opposite sides of the transversal.
• Corresponding angles: Occupy the same relative position at each intersection.

1. For angles \( x \) and \( y \):

• The two lines are parallel, and the transversal intersects them. Angle \( y \) and angle \( x \) are outside the two parallel lines and on opposite sides of the transversal. This matches the definition of alternate exterior angles.
• Same - side interior angles are between the lines and on the same side, so A is incorrect.
• Alternate interior angles are between the lines, so B is incorrect.
• Corresponding angles have the same relative position, so D is incorrect.

Answer:

C. alternate exterior