Question

look at this diagram: if \\( overrightarrow{o q} \\) and \\( overrightarrow{r t} \\) are parallel lines and \\( m \angle t s p=48^{circ} \\), what is \\( m \angle o p s \\)?

Explanation:

Step1: Use the property of adjacent angles

Since \(\overrightarrow{OQ}\) and \(\overrightarrow{RT}\) are parallel lines and \(UN\) is a transversal. \(\angle TSP\) and \(\angle OPS\) are adjacent angles on a straight line. The sum of adjacent angles on a straight line is \(180^{\circ}\).
So, \(m\angle TSP + m\angle OPS=180^{\circ}\)

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

Given \(m\angle TSP = 48^{\circ}\), substitute into the equation:
\(m\angle OPS=180^{\circ}-m\angle TSP\)
\(m\angle OPS = 180^{\circ}- 48^{\circ}\)
\(m\angle OPS=132^{\circ}\)

Answer:

\(132\)