Question

consider the diagram of complementary angles
^--------------------^
|--------------------/
|------------------/
|-------5x------/-------31-------
|--------------/
|------------/
|----------/
|_____|
|_____|________________
part 1: which equation may be used to determine the value of x?
a. 5x-31=90
b. 5x+31=180
c. 5x=31
d. 5x+31=90
part 2: complete the following prompts
x=_
the measure of angle 5x=_ degrees

Answer 1

To solve the problem of complementary angles in the diagram you provided, we need to remember that complementary angles sum up to 90 degrees.

### Part 1: Finding the Equation
If we denote the angle of \(5x\) as one angle and \(31\) as the other angle, we can set up the equation based on the fact that their sum is 90 degrees.

The correct equation is:
\[
5x + 31 = 90
\]
Thus, the answer is:
**d. 5x + 31 = 90**

### Part 2: Solve for \(x\) and find the measure of angle \(5x\)
1. Solve for \(x\):
\[
5x + 31 = 90
\]
Subtract 31 from both sides:
\[
5x = 90 - 31
\]
\[
5x = 59
\]
Now, divide by 5:
\[
x = \frac{59}{5} = 11.8
\]

2. Calculate the measure of angle \(5x\):
\[
5x = 5 \times 11.8 = 59
\]

### Final Answers:
- \(x = 11.8\)
- The measure of angle \(5x = 59\) degrees

So, filling out the prompts:
- x = 11.8
- the measure of angle 5x = 59 degrees