Question

linear pair
alternate exterior
corresponding
vertical
alternate interior
same - side interior

Explanation:

• A linear pair is a pair of adjacent angles that form a straight line. Here, \(x\) and \(y\) are not adjacent in that sense.
• Alternate - exterior angles are formed when a transversal crosses two parallel lines. The angles are on the outside of the two parallel lines and on opposite sides of the transversal. But \(x\) and \(y\) are not in the exterior - alternate position.
• Corresponding angles are in the same relative position. \(x\) and \(y\) do not match the corresponding - angle position.
• Vertical angles are opposite angles formed by the intersection of two lines. \(x\) and \(y\) are not vertical angles.
• Alternate - interior angles are formed when a transversal crosses two parallel lines. The angles are on the inside of the two parallel lines and on opposite sides of the transversal. \(x\) and \(y\) do not meet this criterion.
• Same - side interior angles are on the same side of the transversal and inside the two parallel lines. \(x\) and \(y\) satisfy this condition.

Answer:

same - side interior