line jm intersects line gk at point n. which statements are true about the figure? choose two correct answers. ∠gnj is complementary to ∠jnk. ∠mng is complementary to ∠gnj. ∠gnm is supplementary to ∠jnk. ∠knj is supplementary to ∠mnl. ∠mnl is complementary to ∠knl.

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# Brief Explanations:
1. Analyze $\angle GNJ$ and $\angle JNK$: Since $JM\perp GK$ (right angle at $N$), $\angle GNJ + \angle JNK= 90^\circ$, so they are complementary.
2. Analyze $\angle MNL$ and $\angle KNL$: $\angle MNL+\angle KNL = \angle MNK$, and $\angle MNK = 90^\circ$ (as $JM\perp GK$), so they are complementary.
3. $\angle KNJ$ and $\angle MNL$: $\angle KNJ = 90^\circ+\angle MNL$ (since $\angle MNK = 90^\circ$), so they are not supplementary.
4. $\angle GNM$ and $\angle JNK$: $\angle GNM = 90^\circ$ (straight line $GK$ and $JM$ perpendicular), $\angle JNK = 90^\circ$, their sum is $180^\circ$? No, $90 + 90=180$? Wait, no, $\angle GNM$ and $\angle JNK$: $\angle GNM$ is $90^\circ$ (vertical to $\angle MNK$? Wait, no, $JM$ and $GK$ are perpendicular, so $\angle GNM = 90^\circ$, $\angle JNK = 90^\circ$, but supplementary means sum to $180^\circ$, so this is wrong.
5. $\angle MNG$ and $\angle GNJ$: $\angle MNG+\angle GNJ = 180^\circ$ (straight line $JM$), so they are supplementary, not complementary.

So the correct ones are $\angle GNJ$ is complementary to $\angle JNK$ and $\angle MNL$ is complementary to $\angle KNL$.
# Answer:
A. $\angle GNJ$ is complementary to $\angle JNK$
E. $\angle MNL$ is complementary to $\angle KNL$

(Note: Assuming the options are labeled as A: $\angle GNJ$ is complementary to $\angle JNK$, B: $\angle MNG$ is complementary to $\angle GNJ$, C: $\angle GNM$ is supplementary to $\angle JNK$, D: $\angle KNJ$ is supplementary to $\angle MNL$, E: $\angle MNL$ is complementary to $\angle KNL$)

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