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°.

 

Step-by-Step Solution

1. First, note the measure of ∠KRJ, which is 36°.

2. We need to find an angle whose measure, when added to 36°, equals 90°.

3. Analyze each option:

A.For ∠NRM, its measure is 82°. Since 36° + 82°≠90°, it is not the complement.

B.For ∠SRJ, ∠SRJ=46° + 36° = 82°. Since 36°+82°≠90°, it is not the complement.

C.For ∠KRL, ∠KRL is a right - angle, so its measure is 90°. And 36°+ (90° - 36°)=90°. So, ∠KRL contains the complementary angle to ∠KRJ. The part of ∠KRL that is complementary to ∠KRJ is the angle adjacent to ∠KRJ within ∠KRL.

D.For ∠LRM,  ∠LRM = 44°. Since 36°+44° = 80°≠90°, it is not the complement.