Question

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

Explanation:

Step1: Identify angle - relationship

Since \(m\parallel n\), the angles \((9x - 6)^{\circ}\) and \((x + 16)^{\circ}\) are corresponding angles and are equal. So, we set up the equation \(9x-6=x + 16\).

Step2: Solve the equation for \(x\)

First, subtract \(x\) from both sides: \(9x-x-6=x - x+16\), which simplifies to \(8x-6 = 16\). Then add 6 to both sides: \(8x-6 + 6=16 + 6\), getting \(8x=22\). Finally, divide both sides by 8: \(x=\frac{22}{8}=\frac{11}{4}=2.75\).

Answer:

\(x = 2.75\)