Question

10 fill in the blank 6 points if l || m, then find the value of x and y. (7y - 23)° (23x - 16)° (8x - 21)°

Explanation:

Step1: Use corresponding - angles property

Since \(l\parallel m\), the corresponding - angles are equal. So, \(23x - 16=8x - 21\).
\[

$$\begin{align*} 23x-8x&=-21 + 16\\ 15x&=-5\\ x&=-\frac{5}{15}=-\frac{1}{3} \end{align*}$$

\]

Step2: Use linear - pair property

The angles \((7y - 23)^{\circ}\) and \((23x - 16)^{\circ}\) form a linear - pair. So, \((7y - 23)+(23x - 16)=180\).
Substitute \(x =-\frac{1}{3}\) into the equation:
\[

$$\begin{align*} 7y-23+23\times(-\frac{1}{3})-16&=180\\ 7y-23-\frac{23}{3}-16&=180\\ 7y-(23 + 16+\frac{23}{3})&=180\\ 7y-(39+\frac{23}{3})&=180\\ 7y-(\frac{117 + 23}{3})&=180\\ 7y-\frac{140}{3}&=180\\ 7y&=180+\frac{140}{3}\\ 7y&=\frac{540+140}{3}\\ 7y&=\frac{680}{3}\\ y&=\frac{680}{21} \end{align*}$$

\]

Answer:

\(x =-\frac{1}{3},y=\frac{680}{21}\)