Question

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

Explanation:

Step1: Use property of parallel lines

When two parallel lines \(m\parallel n\) are cut by a transversal, the corresponding - angles are equal. Here, \((4x + 9)^{\circ}\) and \((5x-27)^{\circ}\) are corresponding angles, so we set up the equation \(4x + 9=5x - 27\).
\[4x + 9=5x - 27\]

Step2: Solve the equation for \(x\)

Subtract \(4x\) from both sides of the equation:
\[4x+9-4x=5x - 27-4x\]
\[9=x - 27\]
Then add 27 to both sides:
\[9 + 27=x-27 + 27\]
\[x=36\]

Answer:

\(x = 36\)