Question

su and vx are parallel lines.
which angles are supplementary angles?
∠vwt and ∠vwy ∠vwt and ∠str
∠vwt and ∠xwy ∠vwt and ∠utw

Explanation:

Step1: Recall Supplementary Angles

Supplementary angles are two angles whose sum is \(180^\circ\) (a straight angle). They can be adjacent (forming a linear pair) or non - adjacent.

Step2: Analyze Each Option

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

These two angles form a linear pair (they are adjacent and their non - common sides form a straight line). So, \(\angle VWT+\angle VWY = 180^\circ\), which means they are supplementary. But let's check the other options for completeness.

• Option 2: \(\angle VWT\) and \(\angle STR\)

Since \(SU\parallel VX\) and \(RY\) is a transversal, \(\angle VWT\) and \(\angle STR\) are corresponding angles. Corresponding angles are equal when lines are parallel, not supplementary (unless each is \(90^\circ\), which is not indicated here).

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

\(\angle VWT\) and \(\angle XWY\) are vertical angles (if we consider the intersection of lines). Vertical angles are equal, not supplementary (unless each is \(90^\circ\), which is not indicated here).

• Option 4: \(\angle VWT\) and \(\angle UTW\)

\(\angle VWT\) and \(\angle UTW\) are alternate interior angles (since \(SU\parallel VX\) and \(RY\) is a transversal). Alternate interior angles are equal, not supplementary (unless each is \(90^\circ\), which is not indicated here).

Answer:

\(\angle VWT\) and \(\angle VWY\)