Given: Pair of parallel lines and a transversal with angles x and y.
Required: To determine which type of angles are formed by x and y.
Explanation: Consider the following figure below showing a pair of parallel lines and a transversal
In the figure, line l is parallel to line m, and line n is the transversal.
Further alternate angles are the pair:
[tex](\angle1&\angle8),(\angle2&\angle7),(\angle3&\angle6),(\angle4&\angle5)_[/tex]
The angles lying inside the parallel lines are alternate interior, while the angles lying outside the parallel lines are the alternate exterior.
While the corresponding angles are the pair:
[tex](\angle2&\angle6),(\angle1&\angle5),(\angle3&\angle7),(\angle4&\angle8)[/tex]
Finally, the consecutive interior angles are the pair of non-adjacent angles that lie on the same side of the transversal. In the figure above, the consecutive interior angles are:
[tex](\angle4&\angle6),(\angle3&\angle5)[/tex]
Hence the given pair of angles x and y are consecutive interior angles.
Final Answer: Option D is correct.
