Question

find the value of the variables in the given figure.
(3y - 1)°
40°
(5x)°
x =
y =
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Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, $5x = 40$.

Step2: Solve for $x$

Divide both sides of the equation $5x = 40$ by 5. We get $x=\frac{40}{5}=8$.

Step3: Use corresponding - angle property

The angle $(3y - 1)^{\circ}$ and the $40^{\circ}$ angle are corresponding angles (assuming parallel lines indicated by the arrow - heads), so $3y-1 = 40$.

Step4: Solve for $y$

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

Answer:

$x = 8$, $y=\frac{41}{3}$