Chapter 7, Problem 9PT

To determine

To find: The $x$ and $y$ .

Answer to Problem 9PT

The value of $x$ is $\frac{1}{2}$ and the value of $y$ is $\frac{5}{3}$ .

Explanation of Solution

Given information:

  

Calculation:

From the given figure

Using corollary of congruent parts of parallel lines to set up two equations

  $5x+8=21x$  $\left(1\right)$ .

  $20y-2=17y+3$  $\left(2\right)$ .

Calculating for the value of $x$ from equation $\left(1\right)$ .

  $\begin{array}{c}5x+8=21x\\ 8=21x-5x\\ 8=16x\\ \frac{1}{2}=x\end{array}$

Calculating for the value of $x$ from the equation $\left(2\right)$ .

  $\begin{array}{c}20y-2=17y+3\\ 20y-17y=3+2\\ 3y=5\\ y=\frac{5}{3}\end{array}$

Therefore, the value of $x$ is $\frac{1}{2}$ and the value of $y$ is $\frac{5}{3}$ .