Geometry

Question Analysis

This question involves the concept of supplementary angles.

 

Key Concept Explanation

Supplementary angles are two angles whose measures add up to 180°. Geometrically, they form a straight - line (a straight - angle) around a common vertex.

 

Step - by - Step Solution

1. Analyze each option:

A.∠FXE: ∠FXE and ∠WXG do not form a straight - line around point X. So, they are not supplementary.

 

B.∠GXF: ∠GXF and ∠WXG together form a straight - line around point X. Since a straight - line angle measures 180°, ∠GXF is supplementary to ∠WXG.

 

C.∠EXY: ∠EXY and ∠WXG have no direct relationship to form a 180° sum as they are not adjacent in a way to create a straight - line angle around point X. Thus, it is not supplementary to ∠WXG.

 

D.∠HXW: ∠HXW and ∠WXG do not combine to form a straight - line; their sum is not 180°. So, it is not supplementary to ∠WXG.

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