Final answer:
The value of x, when angles ZSOT and ZTOU are complementary, is calculated by setting their measures equal to 90 degrees and solving for x. The resulting value of x is 34.
Step-by-step explanation:
To find the value of x when the angles ZSOT and ZTOU are complementary, we first need to use the fact that complementary angles add up to 90 degrees. Given that mZSOT = 2x + 4 and mZTOU = x - 16, we can write the equation:
2x + 4 + x - 16 = 90
By combining like terms, the equation simplifies to:
3x - 12 = 90
Adding 12 to both sides gives:
3x = 102
Dividing both sides by 3, we find that:
x = 34
Therefore, the value of x is 34.