Question

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

Complementary angles add up to 90°, supplementary angles add up to 180°.

Step2: Analyze angle - pairs

Since line JM intersects line GK at point N and ∠JNK = 90°, ∠GNJ+∠JNK = 180° (linear - pair), so ∠GNJ is supplementary to ∠JNK. ∠MNL+∠KNL = 90° as ∠MNL and ∠KNL form a right - angle at N. ∠MNG+∠GNJ = 180° (linear - pair), so ∠MNG is supplementary to ∠GNJ. ∠KNJ+∠MNL = 180° (linear - pair), so ∠KNJ is supplementary to ∠MNL. ∠GNM+∠JNK = 180° (linear - pair), so ∠GNM is supplementary to ∠JNK.

Answer:

∠MNL is complementary to ∠KNL, ∠KNJ is supplementary to ∠MNL