Question

which angles are vertical angles?∠vwt and ∠xwy∠vwt and ∠str∠vwt and ∠utr∠vwt and ∠vwy

Explanation:

Step1: Recall the definition of vertical angles

Vertical angles are a pair of non - adjacent angles formed by the intersection of two lines. They are opposite each other.

Step2: Analyze each option

• For \(\angle VWT\) and \(\angle XWY\): These are adjacent angles (they share a common side \(WY\)), so they are not vertical angles.
• For \(\angle VWT\) and \(\angle STR\): When two lines intersect (the line \(YR\) and the line \(SU\) intersect at \(T\), and the line \(YR\) and the line \(VX\) intersect at \(W\), but if we consider the intersection of the lines that form the angles, \(\angle VWT\) and \(\angle STR\) are formed by two intersecting lines (the line \(YR\) and the line \(VX - SU\) (since \(VX\parallel SU\) and \(YR\) is a transversal, but actually, if we consider the lines that form the angles, \(\angle VWT\) and \(\angle STR\) are not formed by the intersection of two lines in the correct way. Wait, no, vertical angles are formed by the intersection of two lines. Let's re - check.
• For \(\angle VWT\) and \(\angle UTR\): These are not formed by the intersection of the same two lines.
• For \(\angle VWT\) and \(\angle XWY\): Adjacent (share a common side \(WY\)).
• The correct pair: \(\angle VWT\) and \(\angle XWY\) are vertical angles. Wait, no, vertical angles are formed when two lines intersect. The line \(VX\) and \(YR\) intersect at \(W\). \(\angle VWT\) and \(\angle XWY\) are non - adjacent and formed by the intersection of lines \(VX\) and \(YR\).

Answer:

\(\angle VWT\) and \(\angle XWY\)