Geometry

Question Analysis

This question involves finding the missing angle. The main focus is on understanding the properties of parallel lines cut by a transversal and the property of angle bisector.

 

Key Concept Explanation:

When two parallel lines are cut by a transversal, corresponding angles are in the same relative position at each intersection. The key property is that corresponding angles are congruent.

 

An angle bisector is a ray, line, or segment that divides an angle into two congruent (equal) parts.

 

Step-by-Step Solution:

∵ AB ∥ CD (Given)

∴ m∠1 = m∠FED (Corresponding Angles Postulate)

∵ m∠1 = 48° (Given)

∴ m∠FED = 48° (Substitution)

∴ m∠FEG + m∠GED = 48° (Angle Addition Postulate)

∵ EG is the angle bisector of ∠FED (Given)

∴ m∠FEG = m∠GED (Definition of Angle Bisector)

∴ 2m∠FEG = 2m∠GE...