Question

find the value of x for which m || n. the value of x for which m || n is

Explanation:

Step1: Set up equation using parallel - line property

When two lines \(m\) and \(n\) are parallel, the corresponding angles (or alternate - interior/alternate - exterior angles depending on the setup) are equal. Here, we assume the two given angles \((3x - 40)^{\circ}\) and \((2x + 12)^{\circ}\) are equal. So, \(3x-40 = 2x + 12\).

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides of the equation: \(3x-2x-40=2x - 2x+12\), which simplifies to \(x-40 = 12\). Then add 40 to both sides: \(x-40 + 40=12 + 40\).

Answer:

\(x = 52\)