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 \( x \):
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Subtract \( 31 \) from both sides:
\[ 5x = 90 - 31 \]
\[ 5x = 59 \]
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Then divide both sides by \( 5 \):
\[ x = \frac{59}{5} = 11.8 \]
Now, to find the measure of angle \( 5x \):
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Substitute \( x = 11.8 \) back into the expression for the angle:
\[ 5x = 5 \times 11.8 = 59 \]
Summary Answer
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Part 1: The equation used to determine \( x \) is \( 5x + 31 = 90 \).
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Part 2:
- \( x = 11.8 \)
- The measure of angle \( 5x = 59 \) degrees.
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