Question

∠x and ∠y are complementary
∠z and ∠w are supplementary
∠w ≅ ∠z
∠w ≅ ∠x

Explanation:

Step1: Recall properties of parallelogram

In a parallelogram \(WXYZ\), \(WX\parallel ZY\) and \(WZ\parallel XY\). Also, in a parallelogram, consecutive angles are supplementary (sum to \(180^{\circ}\)) and opposite angles are equal.

Step2: Analyze each option

• For \(\angle X\) and \(\angle Y\): Since \(WX\parallel ZY\) in parallelogram \(WXYZ\), \(\angle X+\angle Y = 180^{\circ}\) (consecutive - interior angles), so they are supplementary, not complementary (\(\text{complementary angles sum to }90^{\circ}\)).
• For \(\angle Z\) and \(\angle W\): Since \(WZ\parallel XY\) in parallelogram \(WXYZ\), \(\angle Z+\angle W=180^{\circ}\) (consecutive - interior angles), so they are supplementary.
• For \(\angle W\) and \(\angle Z\): In a parallelogram, opposite angles are equal. But \(\angle W\) and \(\angle Z\) are not opposite angles. Actually, \(\angle W+\angle Z = 180^{\circ}\) (because \(WX\parallel ZY\)).
• For \(\angle W\) and \(\angle X\): In a parallelogram, \(\angle W\) and \(\angle X\) are consecutive angles. \(\angle W+\angle X = 180^{\circ}\) (because \(WZ\parallel XY\)), so they are not equal.

Answer:

\(\angle Z\) and \(\angle W\) are supplementary.