To set up an equation to solve for \( x \), we can use the fact that angles \( \angle 5 \) and \( \angle 8 \) are likely related (for instance, they may be supplementary or complementary, or alternate interior angles, depending on how they are positioned). The information provided gives us:
- \( m∠5 = 112° \)
- \( m∠8 = (2x + 8)° \)
Assuming that \( \angle 5 \) and \( \angle 8 \) are supplementary (which means their measures add up to \( 180° \)), we can formulate the equation as follows:
\[ m∠5 + m∠8 = 180° \]
Substituting the measures of the angles into the equation gives us:
\[ 112 + (2x + 8) = 180 \]
Now let's simplify and arrange this equation:
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Combine the constants on the left side: \[ 112 + 8 = 120 \] So the equation becomes: \[ 120 + 2x = 180 \]
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Next, solve for \( x \): Subtract 120 from both sides: \[ 2x = 180 - 120 \] \[ 2x = 60 \] Now, divide by 2: \[ x = 30 \]
Therefore, the equation that we initially formed to solve for \( x \) is:
\[ 112 + (2x + 8) = 180 \]
You can fill in your original request as:
\[ x + 120 = 180 \]
This equation can be solved to find \( x \).
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