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, \(x + 19=9x + 1\).
\[

$$\begin{align*} x+19&=9x + 1\\ 19-1&=9x - x\\ 18&=8x\\ x&=\frac{18}{8}=\frac{9}{4}=2.25 \end{align*}$$

\]

Step2: Use linear - pair property

The angles \((3y + 8)\) and \((9x+1)\) form a linear - pair. Since \(x = 2.25\), then \(9x+1=9\times2.25 + 1=20.25+1 = 21.25\).
And \((3y + 8)+(9x + 1)=180\) (linear - pair of angles). Substitute \(9x + 1 = 21.25\) into the equation:
\[

$$\begin{align*} 3y+8+21.25&=180\\ 3y+29.25&=180\\ 3y&=180 - 29.25\\ 3y&=150.75\\ y&=\frac{150.75}{3}=50.25 \end{align*}$$

\]

Answer:

\(x = 2.25\), \(y = 50.25\)