Question

1. true or false?

$l\parallel m$
$g\parallel n$
$n\parallel w$
$g\parallel w$
$m\parallel g$

Explanation:

Step1: Check \(l\parallel m\)

When two lines are parallel, the consecutive - interior angles are supplementary. For lines \(l\) and \(m\) cut by a transversal, \(122^{\circ}+ 58^{\circ}=180^{\circ}\). So \(l\parallel m\) (True).

Step2: Check \(g\parallel n\)

For lines \(g\) and \(n\), the corresponding angles are equal (\(122^{\circ}\) and \(122^{\circ}\)). By the corresponding - angles postulate, \(g\parallel n\) (True).

Step3: Check \(n\parallel w\)

For lines \(n\) and \(w\), the corresponding angles are equal (\(58^{\circ}\) and \(58^{\circ}\)). By the corresponding - angles postulate, \(n\parallel w\) (True).

Step4: Check \(g\parallel w\)

Since \(g\parallel n\) and \(n\parallel w\), by the transitive property of parallel lines (\(a\parallel b\) and \(b\parallel c\) implies \(a\parallel c\)), \(g\parallel w\) (True).

Step5: Check \(m\parallel g\)

For lines \(m\) and \(g\), the consecutive - interior angles: \(122^{\circ}+122^{\circ}=244
eq180^{\circ}\). So \(m\) and \(g\) are not parallel (False).

Answer:

\(l\parallel m\): True; \(g\parallel n\): True; \(n\parallel w\): True; \(g\parallel w\): True; \(m\parallel g\): False.