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, \(3x - 18=2x + 8\).
\[3x-2x=8 + 18\]
\[x=26\]

Step2: Find the value of \(y\)

We know that \(y\) and \((3x - 18)^{\circ}\) are supplementary angles (linear - pair). First, substitute \(x = 26\) into \(3x-18\): \(3\times26-18=78 - 18=60\).
Since \(y+(3x - 18)=180\) (linear - pair of angles), then \(y=180-(3x - 18)\). Substituting \(x = 26\), we get \(y = 180-60=120\).

Answer:

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