Question

In this figure, ZSOT and ZTOU are

complementary. If mZSOT = 2x + 4 and
mZTOU = x - 16, find x.
S
O
T

Answer 1

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.