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, \(9x - 12=5x - 4\).
\[9x-12 = 5x - 4\]

Step2: Solve the equation for \(x\)

Subtract \(5x\) from both sides: \(9x-5x-12=5x - 5x-4\), which simplifies to \(4x-12=-4\). Then add 12 to both sides: \(4x-12 + 12=-4 + 12\), so \(4x = 8\). Divide both sides by 4: \(x=\frac{8}{4}=2\).

Step3: Find the value of \(y\)

The angle \((9x - 12)^{\circ}\) and \(y^{\circ}\) are supplementary (linear - pair of angles). First, find the value of \((9x - 12)\) when \(x = 2\). \(9x-12=9\times2-12=18 - 12 = 6\). Since \((9x - 12)+y=180\) (linear - pair), then \(y=180-(9x - 12)\). Substituting \(x = 2\), we get \(y=180 - 6=174\).

Answer:

\(x = 2\), \(y=174\)