Question

$$\overleftrightarrow{rt}$$ and $$\overleftrightarrow{uw}$$ are parallel lines.
which angles are alternate interior angles?
$$\angle wvs$$ and $$\angle wvx$$ $$\angle wvs$$ and $$\angle uvx$$
$$\angle wvs$$ and $$\angle rsv$$ $$\angle wvs$$ and $$\angle tsv$$

Explanation:

Step1: Recall alternate interior angles definition

Alternate interior angles are non - adjacent angles that lie between two parallel lines and on opposite sides of a transversal.

Step2: Analyze each option

• For \(\angle WVS\) and \(\angle WVX\): \(\angle WVX\) is not between the parallel lines \(\overleftrightarrow{RT}\) and \(\overleftrightarrow{UW}\), so this is not a pair of alternate interior angles.
• For \(\angle WVS\) and \(\angle UVX\): \(\angle UVX\) is not between the parallel lines \(\overleftrightarrow{RT}\) and \(\overleftrightarrow{UW}\), so this is not a pair of alternate interior angles.
• For \(\angle WVS\) and \(\angle RSV\): \(\angle RSV\) is not on the opposite side of the transversal with respect to \(\angle WVS\) between the parallel lines, so this is not a pair of alternate interior angles.
• For \(\angle WVS\) and \(\angle TSV\): \(\overleftrightarrow{RT}\parallel\overleftrightarrow{UW}\), and \(\angle WVS\) and \(\angle TSV\) lie between \(\overleftrightarrow{RT}\) and \(\overleftrightarrow{UW}\) and on opposite sides of the transversal \(XQ\). So \(\angle WVS\) and \(\angle TSV\) are alternate interior angles.

Answer:

\(\angle WVS\) and \(\angle TSV\)