Two different questions, so I'll split them up.
"What would be the supplement of angle Z if the angle is 42.1 degrees?"
What you need to know here is that two angles that are supplementary are equal to 180 degrees. If you want to find the supplement of an angle, and you have one of the angle measures, you need to subtract it from 180. You have an angle measure of 42.1 degrees. This will be the number you subtract.
180 - 42.1 = 137.9 degrees.
That's the answer to your first question, on to the next question.
"What is the complement of angle Y if the angle is (8x - 20) degrees?"
We will make angle Y equal to "x", and the complement to it will be what you already provided, which is 8x - 20. When two angles are complementary, they equal 90 degrees. Set up an equation with the two angle measures equaling 90 degrees.
x + (8x - 20) = 90.
You start off by combining the like terms in the equation. You can easily combine x and 8x, and turn that into 9x. Your new equation will be like this.
9x - 20 = 90.
Now, add 20 to both sides.
9x = 110.
To find x, divide by 9 on both sides.
110/9 = x.
x = 12.22 (NOT AN EXACT ANSWER, ROUNDED OFF).
That's what you got when you solve for x. Therefore, angle Y will equal around 12.22 degrees. Now you need to find the complement for angle Y. You can always subtract 12.22 from 90, but we want to plug x into (8x - 20) to make sure your answer is correct.
([8*12.22] - 20) = 77.76.
If you add 77.76 and 12.22, you get around 89.98. Remember the 12.22 was not an exact answer, so you can say this adds up to 90 degrees.
The complement of angle Y is equal to 77.76 degrees.