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?

Answer 1

Since lines \( m \) and \( n \) are parallel, the angles \( E \) and \( B \) are corresponding angles, which means they are equal.

We have the following equation based on the angle measures:

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

To solve for \( x \), first, we can rearrange the equation by moving all terms involving \( x \) to one side and constant terms to the other side.

Subtract \( 3x \) from both sides:

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

This simplifies to:

\[
18 = 11x - 8
\]

Next, add \( 8 \) to both sides:

\[
18 + 8 = 11x
\]

\[
26 = 11x
\]

Now, divide both sides by \( 11 \):

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

Thus, the value of \( x \) is

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