Question

look at this diagram: if \\( \overleftrightarrow{mo} \\) and \\( \overleftrightarrow{pr} \\) are parallel lines and \\( m\angle ovl = 56.3 ^ { \circ } \\), what is \\( m\angle rqs? \\)

Explanation:

Step1: Identify vertical angles

Since \( \angle ONL\) and \( \angle RQN\) are vertical angles, \(m\angle RQN=m\angle ONL = 56.3^{\circ}\)

Step2: Use linear - pair property

\(\angle RQS\) and \(\angle RQN\) form a linear pair. So \(m\angle RQS + m\angle RQN=180^{\circ}\)
Substitute \(m\angle RQN = 56.3^{\circ}\) into the equation: \(m\angle RQS=180^{\circ}- 56.3^{\circ}\)

$$m\angle RQS = 123.7^{\circ}$$

Answer:

\(123.7\)