Question

given ( mparallel n ), find the value of x.
answer
( x=)

Explanation:

Step1: Use the property of alternate interior angles

When two parallel lines \(m\parallel n\) are cut by a transversal \(t\), the alternate interior angles are equal. So, \(6x + 2=7x-22\).

Step2: Solve the equation for \(x\)

Subtract \(6x\) from both sides of the equation:
\(6x + 2-6x=7x-22 - 6x\)
\(2=x - 22\)
Then add \(22\) to both sides:
\(2+22=x-22 + 22\)
\(x=24\)

Answer:

\(24\)