Answer:
x = 7
y = 26
z = 6
Explanation:
First, we can use vertical angles to say the angle with measure 10x + 6 is equal to the angle with measure 16x - 36. Because of this, we can set up an equation to solve for x:
10x + 6 = 16x - 36
6 = 6x -36
6x = 42
x = 7
Next, we can realize the angle 10x + 6 and 4y are supplementary and add up to 180 because they form a straight line. We can set up and solve the equation:
10x + 6 + 4y = 180
We found x = 7, so we can plug that in:
70 + 6 + 4y = 180
76 + 4y = 180
4y = 104
y = 26
Now, we can realize that the angle 4y and 16z + 8 are vertical angles; this gives us the equation:
4y = 16z + 8
We found that y = 26, so we can plug that in to get:
104 = 16z + 8
16z = 96
z = 6