ir and ln are parallel lines.
which angles are supplementary angles?
∠nmo and ∠lmj
∠kjh and ∠lmo
∠ijh and ∠kjm
∠kjh and ∠kjm

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# Brief Explanations:
1. Recall the definition of supplementary angles: two angles whose sum is $180^\circ$ (a straight angle).
2. Analyze each option:
   - Option 1: $\angle NMO$ and $\angle LMJ$ are vertical angles (equal), not supplementary (unless each is $90^\circ$, not indicated here).
   - Option 2: $\angle KJH$ and $\angle LMO$: Since $IK \parallel LN$ and $OH$ is a transversal, $\angle LMO$ and $\angle KJH$ – wait, no, let's check the lines. $IK$ and $LN$ are parallel, $OH$ is a transversal. $\angle KJH$ and $\angle KJM$: Wait, no, let's check the last option. Wait, $\angle KJH$ and $\angle KJM$: Wait, $\angle KJH$ and $\angle KJM$ – wait, no, let's re - examine. Wait, $\angle KJH$ and $\angle KJM$: Wait, $IK$ is a vertical line, $OH$ is a transversal. $\angle KJH$ and $\angle KJM$: Wait, no, the last option is $\angle KJH$ and $\angle KJM$? Wait, no, the fourth option is $\angle KJH$ and $\angle KJM$. Wait, actually, $\angle KJH$ and $\angle KJM$: Wait, no, let's think about the straight line. $IK$ is a vertical line, and $OH$ intersects it at $J$. So $\angle IJH$ and $\angle KJH$ are supplementary, but in the options, let's check the fourth option: $\angle KJH$ and $\angle KJM$. Wait, no, maybe I made a mistake. Wait, let's check the angles:

Wait, $\angle KJH$ and $\angle KJM$: Wait, $IK$ is a straight line (vertical), so the sum of $\angle KJH$ and $\angle KJM$ – no, wait, $J$ is on $IK$, so the line $IK$ is straight, so the angle on a straight line is $180^\circ$. Wait, $\angle KJH$ and $\angle KJM$: Wait, no, $\angle KJH$ and $\angle KJM$ – wait, maybe the correct option is $\angle KJH$ and $\angle KJM$? Wait, no, let's check the options again.

Wait, the fourth option is $\angle KJH$ and $\angle KJM$. Let's see: $IK$ is a vertical line, and $OH$ passes through $J$. So $\angle KJH$ and $\angle KJM$ – wait, no, $\angle KJH$ and $\angle IJH$ are supplementary, but $\angle IJH$ and $\angle KJM$ – no. Wait, maybe the correct option is $\angle KJH$ and $\angle KJM$? Wait, no, let's re - evaluate.

Wait, supplementary angles sum to $180^\circ$. Let's check each option:

- $\angle NMO$ and $\angle LMJ$: These are vertical angles (opposite angles formed by intersecting lines), so they are equal. Not supplementary (unless each is $90^\circ$, not given).
- $\angle KJH$ and $\angle LMO$: $\angle LMO$ and $\angle KJH$ – since $IK\parallel LN$, $\angle LMO=\angle KJH$ (corresponding angles), so their sum is not $180^\circ$ (unless each is $90^\circ$).
- $\angle IJH$ and $\angle KJM$: $\angle IJH$ and $\angle KJM$ – $\angle IJH$ and $\angle KJH$ are supplementary, but $\angle KJM$ and $\angle IJH$ – not necessarily.
- $\angle KJH$ and $\angle KJM$: Since $IK$ is a straight line, the sum of $\angle KJH$ and $\angle KJM$ is $180^\circ$ (they form a linear pair, angles on a straight line). So they are supplementary.

# Answer:
$\boldsymbol{\angle KJH}$ and $\boldsymbol{\angle KJM}$ (the fourth option: $\angle KJH$ and $\angle KJM$)

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