Question

3.4.6 check your understanding
in the figure shown, $overline{hx}paralleloverline{sl}$, $mangle hkw=(7x + 16)^{circ}$, $mangle vfw=(2(x + 1))^{circ}$, $mangle fvw=(6y - 6)^{circ}$, and $mangle xdw=(2y - 6)^{circ}$.
determine the values of $x$ and $y$.
$x=
$y=$

Explanation:

Step1: Identify vertical - angle relationship

Since $\angle HKW$ and $\angle VFW$ are vertical angles, they are equal. So we set up the equation $7x + 16=2(x + 1)$.
$7x+16 = 2x + 2$.

Step2: Solve the equation for $x$

Subtract $2x$ from both sides: $7x-2x+16=2x - 2x+2$, which simplifies to $5x+16 = 2$.
Then subtract 16 from both sides: $5x+16 - 16=2 - 16$, giving $5x=-14$.
Divide both sides by 5: $x =-\frac{14}{5}=-2.8$.

Step3: Identify corresponding - angle relationship

Since $\overline{HX}\parallel\overline{SL}$, $\angle FVW$ and $\angle XDW$ are corresponding angles, so they are equal. Set up the equation $6y - 6=2y - 6$.

Step4: Solve the equation for $y$

Subtract $2y$ from both sides: $6y-2y - 6=2y-2y - 6$, which simplifies to $4y-6=-6$.
Add 6 to both sides: $4y-6 + 6=-6 + 6$, resulting in $4y = 0$.
Divide both sides by 4: $y = 0$.

Answer:

$x=-2.8$
$y = 0$