Question

look at this diagram:
if \\( \overleftrightarrow{pr} \\) and \\( \overleftrightarrow{su} \\) are parallel lines and \\( m\angle stv = 65 ^ { \circ } \\), what is \\( m\angle pqt \\)?

Explanation:

Step1: Use vertical - angle property

Since \( \angle STV\) and \( \angle UTO\) are vertical angles, \(m\angle UTO=m\angle STV = 65^{\circ}\).

Step2: Use the property of parallel lines and transversal

Because \( \overrightarrow{PR}\parallel\overrightarrow{SU}\) and \(VO\) is a transversal, \( \angle PQT\) and \( \angle UTO\) are supplementary angles.
The sum of supplementary angles is \(180^{\circ}\). So \(m\angle PQT=180^{\circ}-m\angle UTO\).
Substitute \(m\angle UTO = 65^{\circ}\) into the formula: \(m\angle PQT=180 - 65\).

Answer:

\(115\)