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 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:

∵ m∥n (Given)

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

∵ m∠1 = (3x+10)° and m∠7 = 60° (Given)

∴ 3x + 10 = 60 (Substitution)

∴ 3x = 50 (Subtract 10 f...