Question

given m || n, find the value of x and y.
(6x - 12)° (9x + 12)° y°

Explanation:

Step1: Use angle - relationship of parallel lines

Since \(m\parallel n\), the angles \((6x - 12)^{\circ}\) and \((9x+12)^{\circ}\) are supplementary. So, \((6x - 12)+(9x + 12)=180\).

Step2: Simplify the equation

Combining like - terms in the equation \(6x-12 + 9x+12=180\), we get \(6x+9x=180\), which simplifies to \(15x=180\).

Step3: Solve for \(x\)

Dividing both sides of the equation \(15x = 180\) by 15, we have \(x=\frac{180}{15}=12\).

Step4: Find the value of \(y\)

The angle \(y^{\circ}\) and \((9x + 12)^{\circ}\) are vertical angles. Substitute \(x = 12\) into \((9x+12)\): \(9x+12=9\times12 + 12=108+12 = 120\). Since vertical angles are equal, \(y = 120\).

Answer:

\(x = 12\), \(y=120\)