Question

an engineer is designing a parking lot for a local grocery store. the parking spaces are marked with lines where $overline{xd}paralleloverline{yz}paralleloverline{yf}paralleloverline{lp}$ where $overline{wc}$ is a transversal, as shown, where $mangle cnl=(6x - 17.6)^{circ}$, $mangle fbh=(12y - 22)^{circ}$, and $mangle thr=(3x + 29.2)^{circ}$. label the given angles on the diagram provided.
a. determine the value of $x$.
$mangle cnl=mangle thr$
$6x - 17.6 = 3x+29.2$
b. determine the value of $y$.
$mangle cnl + mangle fbh=180$
$(6x - 17.6)+(12y - 22)=180$

Explanation:

Step1: Solve for x

$6x - 17.6=3x + 29.2$
$6x-3x=29.2 + 17.6$
$3x=46.8$
$x = 15.6$

Step2: Substitute x and solve for y

Substitute $x = 15.6$ into $(6x - 17.6)+(12y - 22)=180$.
$(6\times15.6 - 17.6)+(12y - 22)=180$
$(93.6 - 17.6)+(12y - 22)=180$
$76+12y - 22 = 180$
$12y+54 = 180$
$12y=180 - 54$
$12y = 126$
$y=10.5$

Answer:

a. $x = 15.6$
b. $y = 10.5$