The values of x, y, and z are -10.6, 103, and -45, respectively.
To find the values of x, y, and z, we can use the properties of a rhombus. In a rhombus, all four angles are equal.
Let's equate the given angles to each other:
(-10x-8)° = 98° = (-2z+8)° = (y-5)°
We can solve for x, y, and z one by one.
From the equation (-10x-8)° = 98°, we can isolate x:
-10x - 8 = 98
Add 8 to both sides:
-10x = 106
Divide both sides by -10:
x = -10.6
So, the value of x is -10.6.
Next, let's solve the equation (-10x-8)° = (-2z+8)° to find z:
-10x - 8 = -2z + 8
Add 8 to both sides:
-10x = -2z + 16
Divide both sides by -2:
5x = z - 8
Substitute the value of x we found earlier:
5(-10.6) = z - 8
-53 = z - 8
Add 8 to both sides:
z = -53 + 8
z = -45
So, the value of z is -45.
Finally, let's solve the equation (-2z+8)° = (y-5)° to find y:
-2z + 8 = y - 5
Add 5 to both sides:
-2z + 13 = y
Substitute the value of z we found earlier:
-2(-45) + 13 = y
90 + 13 = y
103 = y
So, the value of y is 103.
In summary, the values of x, y, and z are -10.6, 103, and -45, respectively.