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

48
48

10
10

2611
Start Fraction 26 over 11 End Fraction

132

Answer 1

To find the value of \( x \), we need to set up an equation using the information about the angles given.

Since lines \( m \) and \( n \) are parallel, and angle \( E \) and angle \( B \) are alternate interior angles formed by the transversal (the vertical line intersecting the parallel lines), we can set their measures equal to each other.

So, we have:

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

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

1. First, we'll get all terms involving \( x \) on one side of the equation. Subtract \( 3x \) from both sides:

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

This simplifies to:

\[
18 = 11x - 8
\]

2. Next, we'll isolate the term with \( x \) by adding \( 8 \) to both sides:

\[
18 + 8 = 11x
\]

This simplifies to:

\[
26 = 11x
\]

3. Finally, we divide both sides by \( 11 \):

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

Thus, the value of \( x \) is:

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

So the correct response is \( \frac{26}{11} \).