We are working with a geometric figure where two lines, GK (horizontal) and JM (vertical), intersect at point N, forming a right angle. A third line, NL, extends from point N diagonally.

Let's analyze the given options:

1. Angle GNJ is complementary to Angle JNK:

   • Angle GNJ is formed by line GN and line JN, while angle JNK is formed by line JN and line KN. Since GN and KN are parts of perpendicular lines (forming a right angle at point N), the sum of the angles around point N must be 90 degrees (complementary). This statement is true.

2. Angle MNL is complementary to Angle KNL:

   • Since MNL and KNL are adjacent angles that are formed on the same side of line NL, and their sum should add up to less than 90 degrees (since the lines are not perpendicular), these angles cannot be complementary (sum of 90°). This statement is false.

3. Angle MNG is complementary to Angle GNJ:

   • Both angles MNG and GNJ are formed at point N. Since one is vertical and the other is horizontal, they make up the right angle, which means their sum is 90°, making them complementary. This statement is true.

4. Angle KNJ is supplementary to Angle MNL:

   • Angle KNJ and angle MNL are not on the same line and don’t form a straight line, so they cannot be supplementary (sum of 180°). This statement is false.

5. Angle GNM is supplementary to Angle JNK:

   • Angle GNM and angle JNK are not adjacent or on the same straight line, so they cannot be supplementary (sum of 180°). This statement is false.

Correct statements:

• Angle GNJ is complementary to Angle JNK.
• Angle MNG is complementary to Angle GNJ.

Would you like more details or further clarifications?

Related questions:

1. What are complementary angles, and how do they relate to perpendicular lines?
2. How do you determine if two angles are supplementary?
3. Can two adjacent angles formed by intersecting lines ever be complementary?
4. What is the difference between supplementary and complementary angles?
5. How do vertical and horizontal lines intersect to form right angles?

Tip:

When working with complementary angles, always remember they add up to 90°, while supplementary angles add up to 180°.