Question

For the following figure, given that $l\left|\right|m\left|\right|n$. Find the values of $x,y,$and Z.

Short answer

The values are$x=8,y=4,z=42$ .

Step-by-step solution

Step 1- Check the figure.

Consider the figure.

Step 2- Step description.

Since I is parallel to n and n are bisected by m therefore calculate the values as follows:

$\begin{array}{c}5x-4=3(x+4)\\ 5x-4=3x+12\\ 5x-3x=12+4\\ 2x=16\\ x=8\end{array}$

Since m is parallel to n thus,

$\begin{array}{c}6y+2=2y^2-6\\ 2y^2-6y-8=0\\ y^2-3y-4=0\\ y^2-4y+y-4=0\\ y(y-4)+1(y-4)=0\\ (y-4)(y+1)=0\\ y=-1,4\end{array}$

Step 3- Step description.

Use the property of median as follows:

$\begin{array}{c}6y+2=2y^2-6\\ z=\frac{54+30}{2}\\ z=\frac{84}{2}\\ z=42\end{array}$

Therefore, the values are $x=8,y=4,z=42$.