Question

which lines in the diagram must be parallel? (not drawn to scale) 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 r

Explanation:

Step1: Recall angle - related parallel - line rules

If two lines are cut by a transversal, corresponding angles are equal, alternate - interior angles are equal, or same - side interior angles are supplementary, then the lines are parallel.

Step2: Analyze the given angles

The angle adjacent to the \(133^{\circ}\) angle on line \(q\) is \(180 - 133=47^{\circ}\) (linear - pair of angles).
The \(47^{\circ}\) angle on line \(q\) and the \(47^{\circ}\) angle on line \(r\) are corresponding angles.
Since corresponding angles are equal when two lines are cut by a transversal, line \(q\) and line \(r\) are parallel.
There is no information to suggest that other pairs of lines are parallel based on the given angle measures.

Answer:

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