which lines in the diagram must be parallel? (not drawn to scale) 133° 47° 51° q r s t a only line q and…
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
Answer
Explanation:
Step1: Recall angle - related parallel - line rules
If two lines are cut by a transversal, then corresponding angles are equal, alternate interior angles are equal, and same - side interior angles are supplementary for parallel lines.
Step2: Analyze the given angles
We know that (133^{\circ}+47^{\circ}=180^{\circ}). The (133^{\circ}) angle and the (47^{\circ}) angle are same - side interior angles formed by lines (q) and (r) with a transversal.
Step3: Apply the parallel - line theorem
Since the sum of the same - side interior angles formed by lines (q) and (r) is (180^{\circ}), by the same - side interior angles postulate (if two lines are cut by a transversal and the same - side interior angles are supplementary, then the two lines are parallel), lines (q) and (r) are parallel.
Answer:
A. only line (q) and line (r)