Question

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

Explanation:

Step1: Recall definitions

Same - side interior angles: two angles that are on the same side of the transversal and between the two parallel lines.
Corresponding angles: two angles that are in the same relative position with respect to the parallel lines and the transversal.
Alternate interior angles: two angles that are on opposite sides of the transversal and between the two parallel lines.
Linear pair: two adjacent angles that form a straight line (sum to \(180^{\circ}\)).
Alternate exterior angles: two angles that are on opposite sides of the transversal and outside the two parallel lines.
Vertical angles: two non - adjacent angles formed by the intersection of two lines (they are equal).

Step2: Analyze the position of \(x\) and \(y\)

In the given figure, if we assume the two horizontal lines are parallel and the slanted line is a transversal. Angles \(x\) and \(y\) are on opposite sides of the transversal and between the two parallel lines.

Answer:

alternate interior