Question

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

Explanation:

Step1: Identify angle - relationship

Since \(m\parallel n\), the two angles \((x + 19)^{\circ}\) and \((3x+7)^{\circ}\) are corresponding angles and are equal. So we set up the equation \(x + 19=3x + 7\).

Step2: Solve the equation for \(x\)

First, subtract \(x\) from both sides: \(19=3x - x+7\), which simplifies to \(19 = 2x+7\). Then subtract 7 from both sides: \(19 - 7=2x\), so \(12 = 2x\). Finally, divide both sides by 2: \(x=\frac{12}{2}=6\).

Answer:

\(x = 6\)