To solve the problem we must know about Complementary Angles and Supplementary Angles.
What are Supplementary Angles?
When the sum of two angles measures up to 180° then these angles are known as supplementary angles of each other.
for example, ∠x + ∠y = 180°, therefore, the ∠x and ∠y are the supplementary angles of each other.
What are Complementary Angles?
When the sum of two angles measures up to 90° then these angles are known as complementary angles of each other.
for example, ∠x + ∠y = 90°, therefore, the ∠x and ∠y are the complementary angles of each other.
Given to us
- Line JM intersects line GK at point N.
Complementary Angle in the figure
As we know complementary angles are those angles whose sum measures 90°.
therefore, we need two angles that are less than 90° so that their sum is 90°.
We can observe in the figure that only ∠KNl and ∠MNL are less than 90°, and their sum is ∠MNK that is equal to 90°.
Thus, MNL is complementary to KNL.
Supplementary Angle in the figure
As we know supplementary angles are those angles whose sum measures 180°.
We can observe in the figure that from all the options available only ∠GNM and ∠JNK are equal to 90° each, and their sum is equal to 180°.
Thus, GNM is supplementary to JNK.
Learn more about Complementary Angle:
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