Question

look at this diagram:
if \\( \overleftrightarrow{q s} \\) and \\( \overleftrightarrow{t v} \\) are parallel lines and \\( m \angle s r u=126^{circ} \\), what is \\( m \angle v u r? \\)

Explanation:

Step1: Use the property of consecutive interior angles

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary. That is, \(m\angle SRU + m\angle VUR=180^{\circ}\)

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

Given \(m\angle SRU = 126^{\circ}\), then \(m\angle VUR=180^{\circ}-m\angle SRU\)
Substitute \(m\angle SRU = 126^{\circ}\) into the equation: \(m\angle VUR=180 - 126\)

Answer:

\(54\)