Question

look at this diagram: if \\( \overleftrightarrow{q s} \\) and \\( \overleftrightarrow{t v} \\) are parallel lines and \\( m \angle t u r=122^{circ} \\), what is \\( m \angle q r p \\)?

Explanation:

Step1: Find the adjacent angle of ∠TUR

Adjacent angles on a straight line sum to \(180^{\circ}\). Let \(x\) be the adjacent angle of \(\angle TUR\). So, \(x + 122^{\circ}=180^{\circ}\). Then \(x = 180^{\circ}- 122^{\circ}=58^{\circ}\).

Step2: Use the property of parallel lines and transversal

Since \(\overleftrightarrow{QS}\) and \(\overleftrightarrow{TV}\) are parallel lines and \(WRP\) is a transversal. \(\angle QRP\) and the adjacent angle of \(\angle TUR\) are congruent (corresponding angles). So \(m\angle QRP = 58^{\circ}\).

Answer:

\(58\)