Question

look at this diagram:
if \\( \overleftrightarrow { n p } \\) and \\( \overleftrightarrow { q s } \\) are parallel lines and \\( m \angle s r t = 124 ^ { \circ } \\), what is \\( m \angle q r o \\)?

Explanation:

Step1: Use the linear - pair relationship

We know that \(\angle SRT\) and \(\angle QRO\) form a linear pair. The sum of angles in a linear pair is \(180^{\circ}\). So, we have the equation \(m\angle SRT + m\angle QRO=180^{\circ}\).

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

Given \(m\angle SRT = 124^{\circ}\). Substitute this value into the equation: \(m\angle QRO=180^{\circ}-m\angle SRT\). Then \(m\angle QRO = 180 - 124\). So, \(m\angle QRO=56^{\circ}\).

Answer:

56