Question

and are parallel lines.
select all the pairs of supplementary angles.
and
and
and
and

Explanation:

Step1: Definition of supplementary angles

Supplementary angles are two angles whose sum is \(180^{\circ}\).

Step2: Analyze \(\angle HIG\) and \(\angle JIG\)

Since \(\overrightarrow{HJ}\) is a straight - line, \(\angle HIG+\angle JIG = 180^{\circ}\) (linear pair of angles).

Step3: Analyze \(\angle KLI\) and \(\angle KLN\)

Since \(\overrightarrow{NG}\) is a straight - line, \(\angle KLI+\angle KLN=180^{\circ}\) (linear pair of angles).

Step4: Analyze \(\angle MLN\) and \(\angle KLI\)

Because \(\overleftrightarrow{HJ}\parallel\overleftrightarrow{KM}\), \(\angle MLN=\angle HIL\) (corresponding angles). And \(\angle HIL + \angle KLI=180^{\circ}\) (co - interior angles for parallel lines \(\overleftrightarrow{HJ}\) and \(\overleftrightarrow{KM}\) cut by transversal \(\overleftrightarrow{NG}\)), so \(\angle MLN+\angle KLI = 180^{\circ}\).

Step5: Analyze \(\angle KLI\) and \(\angle MLI\)

Since \(\overrightarrow{KM}\) is a straight - line, \(\angle KLI+\angle MLI = 180^{\circ}\) (linear pair of angles).

Answer:

\(\angle HIG\) and \(\angle JIG\), \(\angle KLI\) and \(\angle KLN\), \(\angle MLN\) and \(\angle KLI\), \(\angle KLI\) and \(\angle MLI\)