Question

question given ( m parallel n ), find the value of ( x ).

Explanation:

Step1: Use the property of alternate interior angles

When two parallel lines \(m\parallel n\) are cut by a transversal, the alternate - interior angles are equal. So, we set up the equation \(6x + 14=8x-8\).

Step2: Solve the equation for \(x\)

Subtract \(6x\) from both sides of the equation:
\(6x + 14-6x=8x-8 - 6x\)
\(14 = 2x-8\)
Add \(8\) to both sides:
\(14 + 8=2x-8 + 8\)
\(22=2x\)
Divide both sides by \(2\):
\(x=\frac{22}{2}\)

Answer:

\(x = 11\)