Question

look at this diagram: if \\( \overleftrightarrow{np} \\) and \\( \overleftrightarrow{qs} \\) are parallel lines and \\( m\angle qro = 115 ^ { \circ } \\), what is \\( m\angle por \\)?

Explanation:

Step1: Use the property of supplementary angles

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

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

Given \(m\angle QRO = 115^{\circ}\), substitute into the equation: \(m\angle POR=180^{\circ}-m\angle QRO\).

$$m\angle POR = 180^{\circ}- 115^{\circ}=65^{\circ}$$

Answer:

\(65\)