Question

look at this diagram:
if \\( \overleftrightarrow { m o } \\) and \\( \overleftrightarrow { p r } \\) are parallel lines and \\( m \angle p q n = 112 ^ { \circ } \\), what is \\( m \angle r q s \\)?

Explanation:

Step1: Find the adjacent angle of ∠PQN

Since ∠PQN and ∠RQN are adjacent angles on a straight - line, and the sum of adjacent angles on a straight - line is \(180^{\circ}\). Let \(m\angle RQN=x\), then \(m\angle PQN + x=180^{\circ}\). Given \(m\angle PQN = 112^{\circ}\), we have \(x = 180^{\circ}-112^{\circ}\).

Step2: Calculate the value of \(x\)

\(x=180 - 112=68^{\circ}\).

Step3: Use the property of vertical angles

\(\angle RQS\) and \(\angle RQN\) are vertical angles. Vertical angles are equal. So \(m\angle RQS=m\angle RQN\).

So \(m\angle RQS = 68^{\circ}\).

Answer:

68