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, 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∠A = m∠AFE (Alternate Interior Angles Theorem)

∵ m∠A = 54° (Given)

∴ m∠AFE = 54° (Substitution)

∵ CD ∥ EF (Given)

∴ m∠C = m∠CFE (Alternate Interior Angles Theorem)

∵ m∠C = 26° (Given)

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