Question

in the parking lot below, the spaces are parallel to one another.
$m\angle1=(8y + 4)^{circ}$ and $m\angle2=(9x + 3)^{circ}$.
determine the values of $x$ and $y$.
$x = \square$ and $y = \square$

Explanation:

Step1: Use vertical - angle property

Since vertical angles are equal, $\angle1$ and the angle adjacent to $\angle2$ (which is $60^{\circ}$) are vertical angles. So $m\angle1 = 60^{\circ}$. Then we set up the equation $8y + 4=60$.

Step2: Solve for $y$

Subtract 4 from both sides of the equation $8y + 4=60$: $8y=60 - 4=56$. Then divide both sides by 8: $y=\frac{56}{8}=7$.

Step3: Use vertical - angle property for $\angle2$

$\angle2$ and the $60^{\circ}$ angle are also vertical angles, so $m\angle2 = 60^{\circ}$. Set up the equation $9x+3 = 60$.

Step4: Solve for $x$

Subtract 3 from both sides of the equation $9x + 3=60$: $9x=60 - 3 = 57$. Then divide both sides by 9: $x=\frac{57}{9}=\frac{19}{3}$.

Answer:

$x=\frac{19}{3}$ and $y = 7$