Question

look at this diagram:
if \\( \overrightarrow { rt } \\) and \\( \overrightarrow { uw } \\) are parallel lines and \\( m \angle rsv = 111 ^ { \circ } \\), what is \\( m \angle tsq \\)?
\\( \square ^ { \circ } \\)

Explanation:

Step1: Use the property of supplementary angles

When two angles are supplementary, their sum is \(180^{\circ}\). Since \(\overrightarrow{RT}\parallel\overrightarrow{UW}\), \(\angle RSV\) and \(\angle TSQ\) are supplementary.
Let \(m\angle TSQ = x\). Then \(m\angle RSV+x = 180^{\circ}\)

Step2: Substitute the value of \(m\angle RSV\)

Given \(m\angle RSV = 111^{\circ}\). Substitute into the equation \(111^{\circ}+x=180^{\circ}\)
Solve for \(x\): \(x=180^{\circ}- 111^{\circ}\)
\(x = 69^{\circ}\)

Answer:

\(69\)