Question

Consider the diagram of complementary angles.



Part 1: Which equation may be used to determine the value of x?

(1 point)
Responses

5x+31=90
5 x plus 31 is equal to 90

5x+31=180
5 x plus 31 is equal to 180

5x−31=90
5 x minus 31 is equal to 90

5x = 31
5x = 31
Question 2
(2 points)
Part 2: Complete the following prompts.

x =

The measure of angle 5x =
degrees.

Answer 1

To determine the value of \( x \) in a scenario involving complementary angles (which sum up to 90 degrees), we should use the equation that sets the expression for an angle equal to 90 degrees.

### Part 1:
The correct equation to determine the value of \( x \) is:
**\( 5x + 31 = 90 \)**

### Part 2:
To find \( x \), we need to solve the equation:

1. Start with the equation:
\[
5x + 31 = 90
\]

2. Subtract 31 from both sides:
\[
5x = 90 - 31
\]
\[
5x = 59
\]

3. Divide by 5:
\[
x = \frac{59}{5} = 11.8
\]

Now, we can find the measure of angle \( 5x \):

1. Substitute \( x = 11.8 \) back into the expression \( 5x \):
\[
5x = 5(11.8) = 59
\]

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