Question

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

Explanation:

Step1: Use corresponding - angles property

Since \(m\parallel n\), the corresponding angles are equal. So, \(3x - 18=2x + 8\).

Step2: Solve for \(x\)

Subtract \(2x\) from both sides of the equation \(3x - 18=2x + 8\). We get \(3x-2x-18=2x - 2x+8\), which simplifies to \(x-18 = 8\). Then add 18 to both sides: \(x=8 + 18=26\).

Step3: Find the value of \(y\)

The angle \((3x - 18)^{\circ}\) and \(y^{\circ}\) are supplementary (linear - pair of angles). First, find the value of \(3x-18\) when \(x = 26\). \(3x-18=3\times26-18=78 - 18 = 60\). Since \((3x - 18)+y=180\) (linear - pair), then \(y=180-(3x - 18)\). Substituting \(x = 26\), we have \(y = 180-60=120\).

Answer:

\(x = 26\), \(y = 120\)