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 l and m are parallel because same side interior angles are supplementary.
lines l and m are parallel because alternate interior angles are supplementary.
lines p and q are parallel because alternate exterior angles are congruent.

Explanation:

Step1: Recall angle - relationship rules for parallel lines

• For two lines cut by a transversal:
• If alternate exterior angles are congruent, the lines are parallel.
• Same - side interior angles being congruent (\(130^{\circ}\) and \(130^{\circ}\) for \(p\) and \(q\) is not a valid rule for parallel lines. The rule for same - side interior angles is that they are supplementary (\(\angle1+\angle2 = 180^{\circ}\)) for parallel lines.
• For lines \(l\) and \(m\), \(130^{\circ}+80^{\circ}=210^{\circ}

eq180^{\circ}\), so the same - side interior angles (if we consider the angles in the context of \(l\) and \(m\) with a transversal) are not supplementary. Also, alternate interior angles supplementary is not a standard rule for parallel lines.

• For lines \(p\) and \(q\), the \(130^{\circ}\) angles are alternate exterior angles.

Answer:

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