Question

$overleftrightarrow{gi}$ and $overleftrightarrow{jl}$ are parallel lines. which angles are supplementary angles? ∠ihk and ∠ihf ∠ihk and ∠lkm ∠ihk and ∠jkh ∠ihk and ∠ghf

Explanation:

Step1: Recall supplementary - angle definition

Two angles are supplementary if their sum is 180 degrees. Adjacent angles that form a straight - line are supplementary.

Step2: Analyze each option

• For $\angle IHK$ and $\angle IHF$: $\angle IHK$ and $\angle IHF$ are adjacent angles and they form a straight - line $\overleftrightarrow{FM}$. So, $\angle IHK+\angle IHF = 180^{\circ}$.
• For $\angle IHK$ and $\angle LKM$: $\angle IHK$ and $\angle LKM$ are vertical angles, and vertical angles are equal, not supplementary.
• For $\angle IHK$ and $\angle JKH$: $\angle IHK$ and $\angle JKH$ are alternate interior angles for parallel lines $\overleftrightarrow{GI}$ and $\overleftrightarrow{JL}$, and they are equal, not supplementary.
• For $\angle IHK$ and $\angle GHF$: $\angle IHK$ and $\angle GHF$ are vertical angles, and vertical angles are equal, not supplementary.

Answer:

$\angle IHK$ and $\angle IHF$