Question

find the value of x, y, and z in the rhombus below. (-8y - 9)° (9x - 5)° 85° (-2z + 1)° answer attempt 1 out of 2 x = y = z =

Explanation:

Step1: Use rhombus angle - property

In a rhombus, opposite angles are equal. So, $9x - 5=85$.

Step2: Solve for $x$

Add 5 to both sides of the equation: $9x=85 + 5=90$. Then divide both sides by 9: $x=\frac{90}{9}=10$.

Step3: Use adjacent - angle property

Adjacent angles in a rhombus are supplementary (sum to 180°). So, $-8y - 9+85 = 180$.

Step4: Simplify the equation for $y$

First, combine like - terms: $-8y+76 = 180$. Then subtract 76 from both sides: $-8y=180 - 76 = 104$. Divide both sides by - 8: $y=\frac{104}{-8}=-13$.

Step5: Use opposite - angle property for $z$

Since opposite angles are equal, $-2z + 1=9x - 5$. Substitute $x = 10$ into the equation: $-2z+1=9\times10 - 5=85$.

Step6: Solve for $z$

Subtract 1 from both sides: $-2z=85 - 1 = 84$. Divide both sides by - 2: $z=\frac{84}{-2}=-42$.

Answer:

$x = 10$, $y=-13$, $z=-42$