Question

Parallel lines e and f are cut by transversal b. What is the value of x?

b
(2x + 18)
18)
e
(4x - 14)
Option 1: 16
Option 2: 50
Option 3: 130
Option 4: 164

Answer 1

To find the value of x for parallel lines e and f cut by transversal b, we set the angle expressions equal because corresponding angles are equal when lines are parallel. Solving the equation 2x + 18 = 4x - 14, we find that x equals 16.

Step-by-step explanation:

The student's question involves finding the value of x when parallel lines e and f are cut by transversal b. The equations given are 2x + 18 for line b and 4x - 14 for line e or f. Since lines e and f are parallel, the corresponding angles formed by the transversal are equal. Therefore, we can set the two expressions equal to each other to find x:

2x + 18 = 4x - 14

By subtracting 2x from both sides and adding 14 to both sides, we get:

32 = 2x

Dividing both sides by 2 gives us:

x = 16

The value of x is 16, which corresponds to Option 1.