Question

look at this diagram: diagram of lines pr, su (parallel) and transversal vqo with points s, u on su; p, r on pr; t on su, q on pr; v, o on vqo if \\( \overleftrightarrow{pr} \\) and \\( \overleftrightarrow{su} \\) are parallel lines and \\( m\angle rqt = 60^\circ \\), what is \\( m\angle stq \\)?

Explanation:

Step1: Identify Angle Relationship

Since \( PR \parallel SU \) and \( VO \) is a transversal, \( \angle RQT \) and \( \angle STQ \) are same - side interior angles. The sum of same - side interior angles is \( 180^{\circ} \).

Step2: Calculate \( m\angle STQ \)

We know that \( m\angle RQT = 60^{\circ} \) and \( m\angle RQT+m\angle STQ = 180^{\circ} \) (same - side interior angles). So, \( m\angle STQ=180^{\circ}-m\angle RQT \). Substitute \( m\angle RQT = 60^{\circ} \) into the formula: \( m\angle STQ = 180 - 60=120^{\circ} \).

Answer:

\( 120 \)