Question

given m||n, find the value of x.

Explanation:

Step1: Identify angle - relationship

Since \(m\parallel n\), the angles \((6x + 2)^{\circ}\) and \((7x-22)^{\circ}\) are either corresponding, alternate - interior or same - side interior angles. In this case, they are corresponding angles and are equal. So we set up the equation \(6x + 2=7x - 22\).

Step2: Solve the equation

Subtract \(6x\) from both sides: \(6x+2-6x=7x - 22-6x\), which simplifies to \(2=x - 22\).
Then add 22 to both sides: \(2 + 22=x-22 + 22\).

Answer:

\(x = 24\)