Based on the given parallelogram, the value of x is 23, the value of y is -32, and the value of z is 20.
How to find values o x y and z
In a parallelogram, opposite angles are congruent. Therefore, set up the following equations based on the given angle measures:
4x - 2 = 90 (Opposite angles: 4x - 2 and 90)
-3y - 6 = 90 (Opposite angles: -3y - 6 and 90)
5z - 10 = 90 (Opposite angles: 5z - 10 and 90)
Solving each equation separately:
4x - 2 = 90:
Add 2 to both sides of the equation, we have:
4x = 92
Dividing both sides by 4
x = 23
-3y - 6 = 90:
Adding 6 to both sides of the equation
-3y = 96
Divide both sides by -3
y = -32
5z - 10 = 90:
Adding 10 to both sides of the equation
5z = 100
Dividing both sides by 5
z = 20
Therefore, the value of x is 23, the value of y is -32, and the value of z is 20.