Question

given m || n, find the value of x and y.
answer attempt 2 out of 2

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

Combine like - terms: \(6x-12 + 9x+12=180\), which simplifies to \(15x=180\).

Step3: Solve for \(x\)

Divide both sides of the equation \(15x = 180\) by 15: \(x=\frac{180}{15}=12\).

Step4: Find the value of \(y\)

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

Answer:

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