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?

a. 26/11
b. 132
c. 48
d. 10

Answer 1

Given that lines m and n are parallel, we can use the property that corresponding angles are equal. In this case, angle E and angle B are corresponding angles.

We are given:
- Angle E = \(3x + 18\)
- Angle B = \(14x - 8\)

Since these angles are equal, we can set up the equation:

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

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

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

\[
18 = 11x - 8
\]

2. Add \(8\) to both sides:

\[
26 = 11x
\]

3. Divide by \(11\):

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

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

The correct answer is:
**a. \(\frac{26}{11}\)**