Question

fh and tk are parallel lines. which angles are supplementary angles? ∠kjg and ∠kjl ∠kjl and ∠hgj ∠fgj and ∠kjg ∠jjl and ∠hge

Explanation:

Step1: Recall the definition of supplementary angles

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

Step2: Analyze \(\angle KJG\) and \(\angle KJL\)

These two angles form a linear pair. A linear pair of angles is supplementary.

Step3: Analyze \(\angle KJL\) and \(\angle HGJ\)

Since \(IK\parallel FH\), \(\angle KJL=\angle HGE\) (corresponding angles). \(\angle HGE\) and \(\angle HGJ\) are supplementary (linear pair). But \(\angle KJL\) and \(\angle HGJ\) are not supplementary directly.

Step4: Analyze \(\angle FGJ\) and \(\angle KJG\)

There is no relation (like linear - pair or other angle - relation due to parallel lines) to show their sum is \(180^{\circ}\).

Step5: Analyze \(\angle IJL\) and \(\angle HGE\)

There is no relation (like linear - pair or other angle - relation due to parallel lines) to show their sum is \(180^{\circ}\).

Answer:

\(\angle KJG\) and \(\angle KJL\)