Question

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

132
132

10
10

2611

Answer 1

Since lines \( m \) and \( n \) are parallel, and angles \( E \) and \( B \) are corresponding angles, they are equal. We can set up the equation:

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

To solve for \( x \), first, we'll rearrange the equation to get all terms involving \( x \) on one side and constant terms on the other:

1. Subtract \( 3x \) from both sides:

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

This simplifies to:

\[
18 = 11x - 8
\]

2. Next, add 8 to both sides:

\[
18 + 8 = 11x
\]

This simplifies to:

\[
26 = 11x
\]

3. Now, divide both sides by 11:

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

To convert this to a decimal, you can divide:

\[
x \approx 2.36
\]

None of the given response options (48, 132, 10, 2611) matches the calculated value of \( x \). It's possible that there was a misinterpretation of the angles or parallel lines' properties.

If you have any more information or context, please share it for a clearer solution!