Geometry

Question Analysis

This question involves the concept of complementary angles.

 

Key Concept Explanation

Complementary angles are two angles whose measures add up to 90°. They are an important concept in geometry for understanding angle relationships.

 

Step-by-Step Solution

1. First, note the measure of ∠LNK is 38°.

2. Analyze each option:

A.For ∠RNO, it measures 38°. Since 38° + 38° = 76° ≠ 90°, it's not the complement.

B.∠SNK: As ∠SNO is 52°, and ∠SNK, ∠LNK and ∠SNO form a straight - line (180°), ∠SNK = 180° - 52°- 38° = 90°. So it's not the complement.

C.∠LNR measures 142°. 38° + 142° = 180°, which means they are supplementary, not complementary.

D.∠SNO measures 52°. Since 38°+52° = 90°, ∠SNO is the complement of ∠LNK....