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 - relation definitions

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

Step2: Analyze ∠GNJ and ∠JNK

Since line JM and line GK intersect at N and ∠GNJ+∠JNK = 90° (as JM and GK are perpendicular), ∠GNJ is complementary to ∠JNK.

Step3: Analyze ∠MNL and ∠KNL

We know that ∠MNL+∠KNL=∠MNG + ∠GNJ+∠JNK+∠KNL. Since ∠MNG + ∠GNJ = 90° and ∠JNK+∠KNL is not necessarily 0, ∠MNL is not complementary to ∠KNL.

Step4: Analyze ∠MNG and ∠GNJ

∠MNG+∠GNJ = 90°, so ∠MNG is complementary to ∠GNJ.

Step5: Analyze ∠KNJ and ∠MNL

∠KNJ and ∠MNL do not add up to 180°.

Step6: Analyze ∠GNM and ∠JNK

∠GNM=∠GNJ + ∠JNM, and ∠GNM+∠JNK≠180°.

Answer:

∠GNJ is complementary to ∠JNK; ∠MNG is complementary to ∠GNJ.