Question

which pair of angles is supplementary?
∠rxz and ∠yxz
∠pxq and ∠rxs
∠yzx and ∠uzt
∠wzx and ∠xyz

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles are two angles whose sum is \(180^{\circ}\).

Step2: Analyze \(\angle RXZ\) and \(\angle YXZ\)

These two angles form a linear pair. A linear pair of angles is adjacent and their non - common sides form a straight line. The sum of angles in a linear pair is \(180^{\circ}\).

Step3: Analyze \(\angle PXQ\) and \(\angle RXS\)

These are not adjacent and there is no indication that their sum is \(180^{\circ}\).

Step4: Analyze \(\angle YZX\) and \(\angle UZT\)

These are vertical angles (equal in measure) and not supplementary (unless each is \(90^{\circ}\), which is not indicated).

Step5: Analyze \(\angle WZX\) and \(\angle XYZ\)

There is no geometric relationship (like forming a linear pair) that would make their sum \(180^{\circ}\).

Answer:

\(\angle RXZ\) and \(\angle YXZ\)