Question

look at this diagram: if \\( \overleftrightarrow { rt } \\) and \\( \overleftrightarrow { uw } \\) are parallel lines and \\( m\angle tsq = 131 ^ { \circ } \\), what is \\( m\angle wvs? \\)

Explanation:

Step1: Find the adjacent angle of ∠TSQ

Since ∠TSQ and ∠TSV are adjacent angles on a straight - line, and the sum of adjacent angles on a straight - line is \(180^{\circ}\).
Let \(m\angle TSV=x\), then \(x + 131^{\circ}=180^{\circ}\), so \(x=180^{\circ}-131^{\circ}=49^{\circ}\).

Step2: Use the property of parallel lines

Because \(RT\parallel UW\) and \(QX\) is a transversal. ∠TSV and ∠WVS are alternate interior angles.
For parallel lines \(RT\) and \(UW\) cut by transversal \(QX\), alternate interior angles are equal. So \(m\angle WVS = m\angle TSV\).

Answer:

\(49\)