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) 26/11 10 132 48

Explanation:

Step1: Identify the relationship between angles

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

Step2: Solve the equation for \(x\)

Subtract \(3x\) from both sides: \(18 = 11x-8\).
Add \(8\) to both sides: \(26 = 11x\).
Divide both sides by \(11\): \(x=\frac{26}{11}\).

Wait, no! Wait, actually, angle \(B\) and angle \(E\) are not vertical angles. Wait, angle \(B\) and angle \(E\) - no, lines \(m\) and \(n\) are parallel. Angle \(B\) and angle \(G\) are corresponding angles (if we consider the transversal). But angle \(E\) and angle \(G\) are vertical angles. So angle \(B\) and angle \(E\) are supplementary (since \(m\parallel n\), consecutive interior angles). Wait, no, no. Wait, angle \(B\) and angle \(E\) - no, angle \(B\) and angle \(F\) are corresponding angles (if lines \(m\) and \(n\) are parallel). Wait, no, looking at the figure, angle \(B\) and angle \(G\) are alternate - exterior angles. Angle \(E\) and angle \(G\) are vertical angles. So angle \(B\) and angle \(E\) are equal (because angle \(B=\) angle \(G\) (alternate - exterior angles, \(m\parallel n\)) and angle \(E = \) angle \(G\) (vertical angles)). So \(3x + 18=14x - 8\).

Subtract \(3x\) from both sides:
\(3x+18-3x=14x - 8-3x\)
\(18 = 11x-8\)
Add \(8\) to both sides:
\(18 + 8=11x-8 + 8\)
\(26=11x\)
\(x = \frac{26}{11}\) is wrong. Wait, no! Wait, another approach: angle \(B\) and angle \(D\) are vertical angles. Angle \(D\) and angle \(F\) are alternate - interior angles (if \(m\parallel n\)). Angle \(F\) and angle \(E\) are vertical angles. Wait, no, the correct property: since \(m\parallel n\), angle \(B\) and angle \(E\) are equal (corresponding angles). So \(3x + 18=14x - 8\)
Subtract \(3x\) from both sides:
\(18=11x - 8\)
Add \(8\) to both sides:
\(18 + 8=11x\)
\(26=11x\) (wrong). Wait, no! Wait, the problem is misread. Wait, angle \(B=(14x - 8)\), angle \(E=(3x + 18)\). Since \(m\parallel n\), angle \(B\) and angle \(E\) are supplementary (consecutive interior angles). So \((14x - 8)+(3x + 18)=180\)

Step1: Expand the equation

\(14x-8 + 3x+18=180\)
\(17x+10 = 180\)

Step2: Solve for \(x\)

Subtract \(10\) from both sides:
\(17x+10-10=180 - 10\)
\(17x=170\)
Divide both sides by \(17\):
\(x = 10\)

Answer:

\(10\)