Question

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

(1 point)
Responses

5x+31=90

5x+31=180

5x = 31

5x−31=90

Question 2
(2 points)
Part 2: Complete the following prompts.

x = ?

The measure of angle 5x = ?
degrees.

Answer 1

To determine the equation that can be used to find the value of \( x \), we often look for an equation that sets the expression for an angle equal to a known value. If, for example, it is given that \( 5x + 31 \) represents an angle, and we know that this angle is equal to \( 90 \) degrees, then the appropriate equation would be:

\[ 5x + 31 = 90 \]

This indicates that the angle measures \( 90 \) degrees.

### Part 2

From the equation \( 5x + 31 = 90 \), we can solve for \( x \):

1. Subtract \( 31 \) from both sides:

\[
5x = 90 - 31
\]

\[
5x = 59
\]

2. Then divide both sides by \( 5 \):

\[
x = \frac{59}{5} = 11.8
\]

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

1. Substitute \( x = 11.8 \) back into the expression for the angle:

\[
5x = 5 \times 11.8 = 59
\]

### Summary Answer

- **Part 1:** The equation used to determine \( x \) is \( 5x + 31 = 90 \).

- **Part 2:**
- \( x = 11.8 \)
- The measure of angle \( 5x = 59 \) degrees.