Question

given: ∠5 and ∠16 are supplementary, ∠2 ≅ ∠18
prove: q || r

Explanation:

Step1: Use the property of supplementary angles

Given \( \angle5\) and \( \angle16\) are supplementary, so \( \angle5+\angle16 = 180^{\circ}\).

Step2: Use the vertical - angle property

\( \angle5=\angle7\) (vertical angles are equal). Then \( \angle7+\angle16 = 180^{\circ}\).

Step3: Use the property of corresponding angles

\( \angle16=\angle11\) (vertical angles are equal). So \( \angle7+\angle11 = 180^{\circ}\).

Step4: Use the property of parallel lines

If the sum of the interior angles on the same side of a transversal is \( 180^{\circ}\), then the two lines are parallel. Here, for lines \( q\) and \( r\) and transversal \( s\) (assuming the relevant transversal from the angle - line relationship in the figure), since \( \angle7+\angle11 = 180^{\circ}\), we can conclude \( q\parallel r\).

Answer:

The proof is completed as above to show \( q\parallel r\).