Geometry

Question Analysis:

This question involves the concept of adjacent angles in a geometric figure. The main focus is on identifying an angle that shares a side and a common vertex with ∠4.

 

Key Concept Explanation:

Adjacent angles are two angles that have a common vertex and a common side, but no common interior points.

 

Step-by-Step Solution:

1. Analyze each option:

For ∠BKR, it does not share a common side with ∠4, so it is not adjacent to ∠4.

For ∠RKQ, it shares the common vertex K with ∠4, but  does not share a common side with ∠4, so it is not adjacent to ∠4.

For ∠1, it does not share a common side with ∠4, so it is not adjacent to ∠4.

For ∠PKQ, it shares the common vertex K and the common side KP with ∠4, so it is adjacent to ∠4.