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, \(7x + 6=9x - 6\).

Step2: Solve the equation for \(x\)

Subtract \(7x\) from both sides: \(6 = 9x-7x - 6\), which simplifies to \(6 = 2x-6\). Then add 6 to both sides: \(2x=6 + 6=12\). Divide both sides by 2, we get \(x = 6\).

Step3: Find the value of \(y\)

The angle \((7x + 6)^{\circ}\) and \(y^{\circ}\) are supplementary (linear - pair of angles). Substitute \(x = 6\) into \(7x+6\), we have \(7\times6+6=42 + 6=48^{\circ}\). Since \(y+(7x + 6)=180\), then \(y=180-(7x + 6)\). Substituting \(x = 6\), \(y = 180 - 48=132^{\circ}\).

Answer:

\(x = 6\), \(y = 132\)