Question

fh and ik are parallel lines. which angles are supplementary angles? ∠hgj and ∠fge ∠ijg and ∠hgj ∠hge and ∠fge ∠kjl and ∠hgj

Explanation:

Step1: Recall the definition of supplementary angles

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

Step2: Analyze \(\angle IJG\) and \(\angle HGJ\)

Since \(\overrightarrow{FH}\parallel\overrightarrow{IK}\) and \(EL\) is a transversal. \(\angle IJG\) and \(\angle HGJ\) are same - side interior angles. For parallel lines \(FH\) and \(IK\) cut by transversal \(EL\), the sum of same - side interior angles is \(180^{\circ}\).

Step3: Analyze other pairs

• For \(\angle HGJ\) and \(\angle FGE\): There is no direct relationship (not linear - pair, not same - side interior etc.) to make their sum \(180^{\circ}\).
• For \(\angle HGE\) and \(\angle FGE\): These are adjacent angles but \(\angle HGE+\angle FGE

eq180^{\circ}\) (they are not a linear pair in the sense of forming a straight line in the context of the parallel - line transversal setup).

• For \(\angle KJL\) and \(\angle HGJ\): There is no geometric relationship (such as parallel - line transversal properties) that would make their sum \(180^{\circ}\).

Answer:

\(\angle IJG\) and \(\angle HGJ\)