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, \(9x - 13=3x - 11+180\) (the non - adjacent angles formed by a transversal with parallel lines).
\[9x-13 = 3x+169\]

Step2: Solve for \(x\)

Subtract \(3x\) from both sides: \(9x - 3x-13=3x - 3x + 169\), which gives \(6x-13 = 169\).
Add 13 to both sides: \(6x-13 + 13=169 + 13\), so \(6x=182\).
Divide both sides by 6: \(x=\frac{182}{6}=\frac{91}{3}\).

Step3: Find \(y\)

\(y\) and \((3x - 11)\) are supplementary angles (linear pair). So \(y=180-(3x - 11)\).
Substitute \(x = \frac{91}{3}\) into the equation for \(y\):
\[y=180-(3\times\frac{91}{3}-11)\]
\[y=180-(91 - 11)\]
\[y=180 - 80\]
\[y = 100\]

Answer:

\(x=\frac{91}{3},y = 100\)