Question

3.4.6 check your understanding
in the figure shown,
$overline{hx} parallel overline{sl},m\angle wfl=(4(4x - 2))^{circ},m\angle wkd=(4x - 12)^{circ},m\angle fvw=(4y - 9)^{circ}$, and $m\angle xdw=(6y - 41)^{circ}$.
find the values of $x$ and $y$.
$x =
$
$y =
$

Explanation:

Step1: Use corresponding - angles property

Since $\overline{HX}\parallel\overline{SL}$, $\angle WFL$ and $\angle WKD$ are corresponding - angles, so they are equal.
$4(4x - 2)=4x-12$

Step2: Expand the left - hand side

Expand $4(4x - 2)$ to get $16x-8$.
The equation becomes $16x - 8=4x-12$.

Step3: Move the $x$ terms to one side

Subtract $4x$ from both sides: $16x-4x - 8=4x-4x-12$, which simplifies to $12x-8=-12$.

Step4: Move the constant terms to one side

Add 8 to both sides: $12x-8 + 8=-12 + 8$, so $12x=-4$.

Step5: Solve for $x$

Divide both sides by 12: $x=-\frac{4}{12}=-\frac{1}{3}$.

Step6: Use vertical - angles property

$\angle FVW$ and $\angle XDW$ are vertical - angles, so they are equal.
$4y-9 = 6y-41$.

Step7: Move the $y$ terms to one side

Subtract $4y$ from both sides: $4y-4y-9=6y-4y-41$, which simplifies to $-9 = 2y-41$.

Step8: Move the constant terms to one side

Add 41 to both sides: $-9 + 41=2y-41 + 41$, so $32 = 2y$.

Step9: Solve for $y$

Divide both sides by 2: $y = 16$.

Answer:

$x=-\frac{1}{3}$
$y = 16$