Question

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

Explanation:

Step1: Use property of corresponding - angles

Since \(m\parallel n\), the corresponding angles are equal. So, \(9x + 2=5x- 18\).
\[9x+2 = 5x - 18\]
\[9x-5x=-18 - 2\]
\[4x=-20\]
\[x = - 5\]

Step2: Use property of alternate - interior angles

The angles \((9x + 2)\) and \((2y + 20)\) are alternate - interior angles. Since \(m\parallel n\), they are equal. First, substitute \(x=-5\) into \(9x + 2\):
\[9x+2=9\times(-5)+2=-45 + 2=-43\]
Then set \(-43=2y + 20\).
\[2y=-43 - 20\]
\[2y=-63\]
\[y=-\frac{63}{2}=-31.5\]

Answer:

\(x=-5,y = - 31.5\)