Question

given (mparallel n), find the value of (x) and (y). (4y - 7)° (6x + 9)° (2x + 3)°

Explanation:

Step1: Use corresponding - angles property

Since \(m\parallel n\), the corresponding angles are equal. So, \(6x + 9=2x+3\).
\[

$$\begin{align*} 6x+9&=2x + 3\\ 6x-2x&=3 - 9\\ 4x&=-6\\ x&=-\frac{6}{4}=-\frac{3}{2} \end{align*}$$

\]

Step2: Use linear - pair property

The angles \((4y - 7)^{\circ}\) and \((6x + 9)^{\circ}\) form a linear - pair, so \((4y-7)+(6x + 9)=180\). Substitute \(x =-\frac{3}{2}\) into the equation:
\[

$$\begin{align*} 4y-7+6\times(-\frac{3}{2})+9&=180\\ 4y-7 - 9+9&=180\\ 4y-7&=180\\ 4y&=180 + 7\\ 4y&=187\\ y&=\frac{187}{4} \end{align*}$$

\]

Answer:

\(x =-\frac{3}{2},y=\frac{187}{4}\)