Question

find the value of x, y, and z in the parallelogram below. (-4x - 1)° (-y - 10)° (4z - 3)° 75° answer attempt 1 out of 2 x = y = z =

Explanation:

Step1: Use opposite - angle property

In a parallelogram, opposite angles are equal. So, $-y - 10=75$.
Solve the equation for $y$:
$-y=75 + 10$
$-y=85$
$y=-85$

Step2: Use adjacent - angle property

Adjacent angles in a parallelogram are supplementary (their sum is $180^{\circ}$). Consider the adjacent angles $-4x - 1$ and $75$.
So, $(-4x - 1)+75 = 180$.
First simplify the left - hand side: $-4x+74 = 180$.
Then, move 74 to the right - hand side: $-4x=180 - 74$.
$-4x=106$.
Solve for $x$: $x=-\frac{106}{4}=-\frac{53}{2}=-26.5$.

Step3: Use opposite - angle property for $z$

Since opposite angles are equal, $4z-3 = -y - 10$.
We know $y=-85$, so $4z-3=-(-85)-10$.
$4z-3 = 85 - 10$.
$4z-3 = 75$.
Add 3 to both sides: $4z=75 + 3$.
$4z=78$.
Solve for $z$: $z=\frac{78}{4}=\frac{39}{2}=19.5$.

Answer:

$x=-26.5$, $y=-85$, $z = 19.5$