Geometry

Question Analysis

This question involves solving for the variable x given two parallel lines cut by a transversal, with angle measures expressed algebraically. The focus is on identifying the relationship between given angles and using it to set up an equation for x.

 

Key Concept Explanation:

When two parallel lines are cut by a transversal, alternate exterior angles are on opposite sides of the transversal and outside the two lines. The key property is that alternate exterior angles are congruent.

 

Step-by-Step Solution:

∵ m∥n (Given)

∴ m∠1 = m∠7 (Alternate Exterior Angles Theorem)

∵ m∠3 = (5x+10)° and m∠5 = (7x-30)° (Given)

∴ 5x + 10 = 7x - 30 (Substitution)

∴ 10 + 30 = 7x - 5x (Subtract 5x from both sides)

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