Question

Use the image to answer the question.

A vertical line is intersected by two parallel lines lower m and lower n forming eight angles.

Lines m and n are parallel. Angle E measures (3x+18) degrees and angle B measures (14x−8) degrees. What is the value of x?

(1 point)
Responses

2611
Start Fraction 26 over 11 End Fraction

132
132

10
10

48

Answer 1

To solve for \( x \) in the given problem, we need to understand the relationship between angles formed by a transversal intersecting two parallel lines.

Given:
- Angle \( E \) = \( 3x + 18 \) degrees
- Angle \( B \) = \( 14x - 8 \) degrees

Since lines \( m \) and \( n \) are parallel, angles \( E \) and \( B \) are alternate interior angles. Therefore, they are equal:

\[
3x + 18 = 14x - 8
\]

Now, we will solve for \( x \):

1. Subtract \( 3x \) from both sides:
\[
18 = 14x - 3x - 8
\]
\[
18 = 11x - 8
\]

2. Add \( 8 \) to both sides:
\[
18 + 8 = 11x
\]
\[
26 = 11x
\]

3. Divide both sides by \( 11 \):
\[
x = \frac{26}{11}
\]

Thus, the value of \( x \) is \( \frac{26}{11} \).

The correct response is:
Start Fraction 26 over 11 End Fraction.