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:

Corresponding angles are in the same relative position at each intersection. The key property is that corresponding angles are congruent.

 

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:

Construct line c through the point of intersection of the two transversals, and construct it parallel to line a. (Auxiliary Line)

∵ a ∥ c (By construction)

∴ m∠1 = m∠4 (Corresponding Angles Postulate)

∵ a ∥ b (Given)

∵ a ∥ c (By construction)

∴ b ∥ c (Transitive Property of Parallel Lines)

∴ m∠2 = m∠5 (Alternate Interior Angles Theo...