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 angle - relationship definitions

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

Step2: Analyze each option

• For ∠GNJ and ∠JNK: ∠GNJ+∠JNK = 180° (linear - pair), so they are supplementary, not complementary.
• For ∠MNL and ∠KNL: ∠MNL+∠KNL=90° (since JM⊥GK at N and ∠MNL and ∠KNL make up the right - angle ∠MNK), so ∠MNL is complementary to ∠KNL.
• For ∠MNG and ∠GNJ: ∠MNG + ∠GNJ=90° (since JM⊥GK at N), so ∠MNG is complementary to ∠GNJ.
• For ∠KNJ and ∠MNL: There is no fixed 180° relationship between them.
• For ∠GNM and ∠JNK: ∠GNM = 90°, ∠JNK is not 90°, and ∠GNM+∠JNK≠180°.

Answer:

∠MNL is complementary to ∠KNL; ∠MNG is complementary to ∠GNJ