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.

 

Key Concept Explanation:

When two parallel lines are cut by a transversal:

Same-side interior angles are on the same side of the transversal and inside the two lines. The key property is that same-side interior angles are supplementary.

 

Alternate interior angles are on opposite sides of the transversal and inside the two lines. The key property is that alternate interior angles are congruent.

 

Step-by-Step Solution:

∵ AB ∥ CD ∥ EF (Given)

∴ AB ∥ EF (Transitive Property of Parallel Lines)

∴ m∠FBA + m∠F = 180° (Same-side Interior Angles Theorem)

∵ m∠F = 128° (Given)

∴ m∠FBA + 128° = 180° (Substitution)

∴ m∠FBA = 180° - 128° = 52° (Subtraction)

∵ AB ∥ CD (Given)

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