Question

given m||n, find the value of x. (3x - 28)° (x + 2)°

Explanation:

Step1: Identify angle - relationship

Since \(m\parallel n\), the angles \((3x - 28)^{\circ}\) and \((x + 2)^{\circ}\) are alternate - interior angles, and alternate - interior angles are equal. So we set up the equation \(3x-28=x + 2\).

Step2: Solve the equation for \(x\)

First, subtract \(x\) from both sides: \(3x-x-28=x - x+2\), which simplifies to \(2x-28 = 2\).
Then, add 28 to both sides: \(2x-28 + 28=2 + 28\), getting \(2x=30\).
Finally, divide both sides by 2: \(x=\frac{30}{2}=15\).

Answer:

\(x = 15\)