Question

use the image to answer the 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?

Explanation:

Step1: Identify angle - relationship

Since lines \(m\) and \(n\) are parallel, angle \(E\) and angle \(B\) are corresponding angles and are congruent. So, \(3x + 18=14x - 8\).

Step2: Solve the equation for \(x\)

First, move the \(x\) - terms to one side and the constants to the other side. Subtract \(3x\) from both sides: \(18 = 14x-3x - 8\), which simplifies to \(18 = 11x - 8\). Then add 8 to both sides: \(18 + 8=11x\), so \(26 = 11x\). Finally, divide both sides by 11: \(x=\frac{26}{11}\).

Answer:

\(x = \frac{26}{11}\)