Question

3-2 algebra and parallel lines and transversals practice
find the value of each variable in the figure below.
***just type the number and nothing else.
(3y - 1)°
40°
z°
(5x)°
x =
y =
z =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Since the angle of $40^{\circ}$ and $(3y - 1)^{\circ}$ are vertical angles, we set up the equation $3y-1 = 40$.

Step2: Solve for y

Add 1 to both sides of the equation: $3y=40 + 1=41$, then $y=\frac{41}{3}$.

Step3: Use corresponding - angle property

The angle of $(5x)^{\circ}$ and the $40^{\circ}$ angle are corresponding angles (assuming parallel lines). So we set up the equation $5x=40$.

Step4: Solve for x

Divide both sides of the equation by 5: $x = 8$.

Step5: Use linear - pair property

The angle of $z^{\circ}$ and the $40^{\circ}$ angle form a linear - pair (sum to $180^{\circ}$). So $z=180 - 40=140$.

Answer:

$x = 8$
$y=\frac{41}{3}$
$z = 140$