Question

which lines in the diagram must be parallel? (not drawn to scale) 133° 47° 51° q r s t a only line q and line r b only line q and line s c only line r and line s d only line u and line t

Explanation:

Step1: Recall angle - parallel line relationships

If two lines are cut by a transversal, certain angle relationships indicate parallel lines. Supplementary angles (sum to 180°) and equal - measure corresponding, alternate - interior, or alternate - exterior angles are key.

Step2: Analyze angles related to line \(q\) and \(r\)

The angle adjacent to the 133° angle on line \(q\) is \(180 - 133=47^{\circ}\) (linear - pair of angles). This 47° angle and the 47° angle formed by line \(r\) and the transversal are corresponding angles. Since corresponding angles are equal, line \(q\) and line \(r\) are parallel.

Step3: Check other line pairs

For line \(q\) and \(s\), there is no clear angle relationship (like equal corresponding, alternate - interior/exterior or supplementary angles) that would prove them parallel. For line \(r\) and \(s\), there is no such relationship either. For line \(u\) and \(t\), the 51° angle does not create a relationship with other angles to prove them parallel.

Answer:

A. only line \(q\) and line \(r\)