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, 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.

 

Step-by-Step Solution:

∵ m∥n (Given)

∴ m∠4 + m∠7 = 180° (Same-Side Interior Angles Theorem)

∵ m∠4 = (9x - 7)° and m∠7 = (2x - 22)° (Given)

∴ (9x - 7) + (2x - 22) = 180 (Substitution)

11x - 29 = 180 (Algebraic...