Geometry

Question Analysis

This question involves solving for the variables x and y 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 and y.

 

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.

 

Vertical angles (formed by intersecting lines) are always congruent, regardless of whether the intersecting lines are parallel or not.

 

Step-by-Step Solution:

Set up equations:

In this problem, the angles (4x + 6)° and (7y + 5)° are vertical angles, so we can set their measures equal to each other:

4x + 6 = 7y + 5

 

The angles (7y + 5)° and 6(x - 10)° are corresponding angles, so we can set their measures equal to each other:

7y + 5 = 6(x - 10)

 

Solve for x and y:

Since 4x + 6 = 7y + 5 = 6(x - 10)

We have

4x + 6 = 6(x - 10)