Question

line jm intersects line gk at point n. which statements are true about the figure? select tv options

∠gnj is complementary to ∠jnk

∠mnl is complementary to ∠knl

∠mng is complementary to ∠gnj

∠knj is supplementary to ∠mnl

∠gnm is supplementary to ∠jnk

Explanation:

Step1: Recall the definitions of complementary and supplementary angles

Complementary angles add up to $90^{\circ}$, and supplementary angles add up to $180^{\circ}$.

Step2: Analyze each option

• For $\angle GNJ$ and $\angle JNK$: There is no indication that they add to $90^{\circ}$, so they are not complementary.
• For $\angle MNL$ and $\angle KNL$: Since $\angle JNK = 90^{\circ}$ (right - angle formed by perpendicular lines in the figure), and $\angle MNL+\angle KNL=\angle MNK = 90^{\circ}$ (because $\angle JNM = 180^{\circ}$ and $\angle JNK = 90^{\circ}$, so $\angle MNK=90^{\circ}$), so $\angle MNL$ is complementary to $\angle KNL$.
• For $\angle MNG$ and $\angle GNJ$: $\angle MNG+\angle GNJ=\angle MNJ = 180^{\circ}$ (linear pair), so they are supplementary, not complementary.
• For $\angle KNJ$ and $\angle MNL$: There is no relation that makes their sum $180^{\circ}$.
• For $\angle GNM$ and $\angle JNK$: $\angle GNM+\angle JNK=\angle GNM + 90^{\circ}$. Since $\angle GNM+\angle JNK+\angle GNJ= 180^{\circ}+90^{\circ}$ (full - circle around point $N$ concept, but more simply, $\angle GNM+\angle JNK = 180^{\circ}$ (because $\angle GNM+\angle GNJ = 180^{\circ}$ (linear pair) and $\angle JNK=\angle GNJ$ (vertical angles are equal in a right - angled intersection situation)), so $\angle GNM$ is supplementary to $\angle JNK$.

Answer:

$\angle MNL$ is complementary to $\angle KNL$; $\angle GNM$ is supplementary to $\angle JNK$