Question

Line JM intersects line GK at point N.

Horizontal line G K intersects vertical line J M at point N, forming a right angle. A line extends from point N to L, down and to the right.
Which statements are true about the figure? Select two options.

AngleGNJ is complementary to AngleJNK.
AngleMNL is complementary to AngleKNL.
AngleMNG is complementary to AngleGNJ.
AngleKNJ is supplementary to AngleMNL.
AngleGNM is supplementary to AngleJNK.

Answer 1

The true statements are:

- Angle MNL is complementary to Angle KNL.
Reason: NK and NM are perpendicular, so NL splits that right angle into two angles whose measures add to 90°.

- Angle GNM is supplementary to Angle JNK.
Reason: ∠GNM is a right angle (left vs. down) and ∠JNK is a right angle (up vs. right); 90° + 90° = 180°, so they are supplementary.