Question

look at this diagram:
if \\( \overleftrightarrow { m o } \\) and \\( \overleftrightarrow { p r } \\) are parallel lines and \\( m \angle r q n = 56 ^ { \circ } \\), what is \\( m \angle r q s \\)?
work it out
not feeling ready yet? these can help:
transversals of parallel lines: name angle pairs
find measures of complementary, supplementary, vertical, and adj-
lesson: transversals of parallel lines
lesson: vertical angles

Explanation:

Step1: Use the property of supplementary angles

Since \(\angle RQN\) and \(\angle RQS\) are supplementary angles (they form a linear - pair), and the sum of supplementary angles is \(180^{\circ}\).
We have the formula \(m\angle RQN + m\angle RQS=180^{\circ}\)

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

Given \(m\angle RQN = 56^{\circ}\), substitute into the formula:
\(m\angle RQS=180^{\circ}-m\angle RQN\)
\(m\angle RQS = 180^{\circ}- 56^{\circ}\)
\(m\angle RQS=124^{\circ}\)

Answer:

\(124\)