Question

1. what is line r called and what are ∠1 and ∠2?

line r is the perpendicular bisector and ∠1 and ∠2 are a linear pair
line r is the perpendicular bisector and ∠1 and ∠2 are consecutive interior angles
line r is the transversal and ∠1 and ∠2 are a linear pair
line r is the transversal and ∠1 and ∠2 are consecutive interior angles

Explanation:

Step1: Recall the definition of a transversal

A transversal is a line that intersects two or more other lines. Here, line \(r\) intersects lines \(p\) and \(q\), so line \(r\) is a transversal.

Step2: Recall the definition of consecutive interior angles

Consecutive interior angles (also known as same - side interior angles) are two angles that lie between the two intersected lines (lines \(p\) and \(q\)) and on the same side of the transversal (\(r\)). \(\angle1\) and \(\angle2\) lie between \(p\) and \(q\) and on the same side of \(r\). A linear pair of angles are adjacent angles that form a straight line (sum to \(180^{\circ}\) and share a common side and vertex, which is not the case here as \(\angle1\) and \(\angle2\) do not share a common side). A perpendicular bisector is a line that is perpendicular to another line and bisects it (there is no indication of perpendicularity here).

Answer:

Line \(r\) is the transversal and \(\angle1\) and \(\angle2\) are consecutive interior angles.