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:

\(x = 36\)