Question

Identify each pair of angles as corresponding, alternate interior, alternate exterior, consecutiveinterior, vertical, or adjacent. Explain step-by-step

Answer 1

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.

Step-by-step 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:

`(\angle1&\angle8),(\angle2&\angle7),(\angle3&\angle6),(\angle4&\angle5)_`

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:

`(\angle2&\angle6),(\angle1&\angle5),(\angle3&\angle7),(\angle4&\angle8)`

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:

`(\angle4&\angle6),(\angle3&\angle5)`

Hence the given pair of angles x and y are consecutive interior angles.

Final Answer: Option D is correct.