Question

in the parking lot below, the spaces are parallel to one another. m∠1=(7y - 3)° and m∠2=(7x + 15)°. determine the values of x and y. x = and y =

Explanation:

Step1: Use angle - relationship

Since the parking - lot spaces are parallel, $\angle1$ and the $60^{\circ}$ angle are supplementary (linear pair), so $m\angle1 = 180 - 60=120^{\circ}$. Also, $\angle2$ and the $60^{\circ}$ angle are corresponding angles, so $m\angle2 = 60^{\circ}$.

Step2: Solve for $y$

Set up the equation for $\angle1$: $7y−3 = 120$. Add 3 to both sides: $7y=120 + 3=123$. Then divide both sides by 7: $y=\frac{123}{7}\approx17.57$.

Step3: Solve for $x$

Set up the equation for $\angle2$: $7x + 15=60$. Subtract 15 from both sides: $7x=60 - 15 = 45$. Then divide both sides by 7: $x=\frac{45}{7}\approx6.43$.

Answer:

$x=\frac{45}{7}$, $y=\frac{123}{7}$