Question

question given m || n, find the value of x and y.

Explanation:

Step1: Use property of parallel lines

Since \(m\parallel n\), the angles \((6x + 13)^{\circ}\) and \((7x-5)^{\circ}\) are supplementary (same - side interior angles), so \((6x + 13)+(7x - 5)=180\).
\[6x+13 + 7x-5=180\]
\[13x + 8=180\]
\[13x=180 - 8\]
\[13x=172\]
\[x = \frac{172}{13}\approx13.23\]

Step2: Find the value of \(y\)

The angle \(y^{\circ}\) and \((7x - 5)^{\circ}\) are vertical angles, so \(y=7x-5\). Substitute \(x=\frac{172}{13}\) into the equation for \(y\).
\[y = 7\times\frac{172}{13}-5=\frac{1204}{13}-\frac{65}{13}=\frac{1204 - 65}{13}=\frac{1139}{13}\approx87.62\]

Answer:

\(x=\frac{172}{13}\), \(y=\frac{1139}{13}\)