Question

applying angle relationships to justify parallel lines
which lines are parallel? justify your answer.
lines p and q are parallel because same side interior angles are congruent.
lines p and q are parallel because alternate exterior angles are congruent
lines l and m are parallel because same side interior angles are supplementary
lines l and m are parallel because alternate interior angles are supplementary.

Explanation:

• For Lines \(p\) and \(q\):
• Same - side interior angles: If two lines are cut by a transversal, same - side interior angles are supplementary (\(180^{\circ}\)) for parallel lines. Here, the angles related to \(p\) and \(q\) (if we assume a transversal) do not follow the same - side interior angle property (they are not supplementary in a way that would make \(p\) and \(q\) parallel).
• Alternate exterior angles: Alternate exterior angles are congruent when two parallel lines are cut by a transversal. The \(130^{\circ}\) angles (one associated with \(p\) and one with \(q\)) are alternate exterior angles.
• For Lines \(l\) and \(m\):
• Same - side interior angles: The sum of the angles \(130^{\circ}\) and \(80^{\circ}\) (if we consider them as same - side interior angles for \(l\) and \(m\)) is \(130 + 80=210

eq180\), so they are not supplementary (a requirement for same - side interior angles to prove parallelism).

• Alternate interior angles: Alternate interior angles are not supplementary for parallel lines (they are congruent for parallel lines cut by a transversal).

Answer:

Lines \(p\) and \(q\) are parallel because alternate exterior angles are congruent.