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

48
48

10
10

2611
Start Fraction 26 over 11 End Fraction

132

Answer 1

Since lines \( m \) and \( n \) are parallel, the angles formed by the intersection of the vertical line with the parallel lines can be classified based on their relationships to each other. In this case, angle \( E \) and angle \( B \) are alternate interior angles, which means they are equal.

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

Since \( \angle E \) and \( \angle B \) are equal, we set up the equation:

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

Now, let's solve for \( x \):

1. First, rearrange the equation to isolate \( x \):

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

\[
3x + 26 = 14x
\]

2. Next, subtract \( 3x \) from both sides:

\[
26 = 14x - 3x
\]

\[
26 = 11x
\]

3. Now, divide both sides by 11:

\[
x = \frac{26}{11}
\]

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

**Final Answer: \( \frac{26}{11} \)**