Question

which angles are supplementary angles?
∠vwy and ∠utr ∠vwy and ∠xwt
∠vwy and ∠xwy ∠vwy and ∠stw

Explanation:

Step1: Recall Supplementary Angles

Supplementary angles are two angles whose sum is \(180^\circ\) (a straight angle). They often form a linear pair (adjacent angles on a straight line) or are related by parallel lines and transversals.

Step2: Analyze Each Option

• Option 1: \(\angle VWY\) and \(\angle UTR\)

Check if they sum to \(180^\circ\). From the diagram, \(\angle UTR\) and \(\angle STW\) are vertical angles, but \(\angle VWY\) and \(\angle UTR\) do not form a linear pair or supplementary relationship.

• Option 2: \(\angle VWY\) and \(\angle XWT\)

\(\angle XWT\) and \(\angle VWY\) – are they supplementary? \(\angle XWT\) and \(\angle VWY\) do not form a straight line.

• Option 3: \(\angle VWY\) and \(\angle XWY\)

\(\angle VWY\) and \(\angle XWY\): These two angles form a linear pair (they are adjacent and lie on a straight line \(VX\) and \(RY\) intersecting at \(W\)). A linear pair of angles is supplementary, so their sum is \(180^\circ\).

• Option 4: \(\angle VWY\) and \(\angle STW\)

\(\angle STW\) and \(\angle UTR\) are vertical angles, but \(\angle VWY\) and \(\angle STW\) do not sum to \(180^\circ\).

Answer:

\(\angle VWY\) and \(\angle XWY\) (the third option: \(\boldsymbol{\angle VWY}\) and \(\boldsymbol{\angle XWY}\))