Question

which lines in the diagram must be parallel? (not drawn to scale) 133° 47° 51° 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: Find the supplementary angle of \(133^{\circ}\)

The supplementary angle of \(133^{\circ}\) is \(180^{\circ}- 133^{\circ}=47^{\circ}\).

Step2: Use the converse of corresponding angles postulate

Since the angle adjacent to \(133^{\circ}\) (which is \(47^{\circ}\)) and the given \(47^{\circ}\) angle are corresponding angles, by the converse of corresponding angles postulate, line \(q\) and line \(r\) are parallel.

Answer:

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