Question

look at this diagram:
if \\( \overleftrightarrow { r t } \\) and \\( \overleftrightarrow { u w } \\) are parallel lines and \\( m \angle r s v = 111 ^ { \circ } \\), what is \\( m \angle w v s \\)?

Explanation:

Step1: Use the property of consecutive interior angles

Since \( \overleftrightarrow{RT} \parallel \overleftrightarrow{UW} \), \( \angle RSV\) and \( \angle WVS\) are consecutive interior angles.
The sum of consecutive interior angles is \(180^{\circ}\).
So, \(m\angle RSV + m\angle WVS=180^{\circ}\).

Step2: Solve for \(m\angle WVS\)

Given \(m\angle RSV = 111^{\circ}\), substitute into the equation:
\(111^{\circ}+m\angle WVS = 180^{\circ}\).
Then \(m\angle WVS=180^{\circ}- 111^{\circ}\).
\(m\angle WVS = 69^{\circ}\).

Answer:

\(69\)