Question

which angles are alternate exterior angles?
∠utw and ∠vwt
∠str and ∠stw
∠vwy and ∠utr
∠xwt and ∠utr
su and vx are parallel lines.
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Explanation:

Step1: Recall the definition of alternate exterior angles

Alternate exterior angles are non - adjacent exterior angles that lie on opposite sides of the transversal.

Step2: Analyze each pair

• For \(\angle UTW\) and \(\angle VWT\): These are interior angles, not exterior angles.
• For \(\angle STR\) and \(\angle STW\): These are adjacent angles, not alternate exterior angles.
• For \(\angle VWY\) and \(\angle UTR\):
• \(SU\) and \(VX\) are parallel lines and \(YR\) is the transversal.
• \(\angle VWY\) and \(\angle UTR\) are non - adjacent exterior angles and lie on opposite sides of the transversal \(YR\).
• For \(\angle XWT\) and \(\angle UTR\): \(\angle XWT\) is an interior angle (if we consider the parallel lines \(SU\) and \(VX\) and transversal \(YR\)), so this pair does not satisfy the definition of alternate exterior angles.

Answer:

\(\angle VWY\) and \(\angle UTR\)