Question

select all the pairs of supplementary angles.
∠ghk and ∠ihk
∠ihk and ∠jkh
∠lkm and ∠lkh
∠ihk and ∠ghf

Explanation:

Step1: Recall Supplementary Angles Definition

Supplementary angles are two angles whose sum is $180^\circ$ (a straight angle).

Step2: Analyze $\angle GHK$ and $\angle IHK$

From the diagram, $\angle GHK$ and $\angle IHK$ form a linear pair (they are adjacent and form a straight line). So their sum is $180^\circ$, meaning they are supplementary.

Step3: Analyze $\angle IHK$ and $\angle JKH$

Lines $GI$ and $JL$ are parallel (implied by the diagram's structure, as $IH$ and $KL$ are parallel, and $GH$ and $JK$ are parallel). $\angle IHK$ and $\angle JKH$ are same - side interior angles? Wait, no, actually, since $GH$ and $JK$ are a straight line (collinear), and $IH$ and $KL$ are parallel, but more directly, $\angle IHK$ and $\angle JKH$: looking at the transversal $HK$, $\angle IHK$ and $\angle JKH$: wait, actually, $\angle IHK$ and $\angle JKH$: since $GI$ and $JL$ are parallel, and $HK$ is a transversal, but also, if we consider the straight line formed by $G - H - I$ and $J - K - L$, $\angle IHK$ and $\angle JKH$: actually, $\angle IHK+\angle JKH = 180^\circ$ because they are same - side interior angles for parallel lines $GI\parallel JL$ and transversal $HK$. So they are supplementary.

Step4: Analyze $\angle LKM$ and $\angle LKH$

$\angle LKM$ and $\angle LKH$: these two angles are adjacent but form a right angle? No, from the diagram, they seem to be complementary or just not supplementary. Their sum is not $180^\circ$.

Step5: Analyze $\angle IHK$ and $\angle GHF$

$\angle IHK$ and $\angle GHF$: $\angle GHF$ and $\angle GHK$ are vertical angles? Wait, $\angle GHF$ and $\angle KHM$ are vertical angles. $\angle IHK$ and $\angle GHF$: their sum is not $180^\circ$ as they are not a linear pair or related by parallel lines to sum to $180^\circ$.

Answer:

$\angle GHK$ and $\angle IHK$, $\angle IHK$ and $\angle JKH$