Geometry

Question Analysis

This question involves the geometric concept of supplementary angles.

 

Key Concept Explanation

Supplementary angles are two angles whose measures add up to 180°. In a diagram with intersecting lines, angles that form a linear pair (lie on a straight - line) are supplementary.

 

Step - by - Step Solution

1. Analyze the angles around point N:

A linear pair of angles is formed when two lines intersect and the adjacent angles combine to form a straight line.

For ∠RNS, the angle that forms a linear pair with it is ∠SNK. Since they together lie on a straight line, by the definition of supplementary angles, ∠SNK is supplementary to ∠RNS.

 

2. Evaluate the other options:

B.∠KNL: It does not form a linear pair with ∠RNS, so it is not supplementary to ∠RNS.

C.∠RNL: This angle does not form a linear pair with ∠RNS, so it is not the supplementary angle.

D.∠SNO: ∠SNO and ∠RNS do not form a linear pair, so it is not supplementar...