To solve for \( x \) given \( m∠5 = 112° \) and \( m∠8 = (2x + 8)° \), we need to determine the relationship between these two angles.
If angles 5 and 8 are supplementary (they add up to 180°), we can set up the following equation:
\[ m∠5 + m∠8 = 180° \]
Substituting the known values gives us:
\[ 112° + (2x + 8)° = 180° \]
To solve for \( x \), we can simplify this equation:
- Combine the constant terms:
\[ 112 + 8 = 120 \] So the equation becomes: \[ 120 + 2x = 180 \]
- Subtract 120 from both sides:
\[ 2x = 180 - 120 \] \[ 2x = 60 \]
- Divide by 2:
\[ x = 30 \]
Thus, the equation to solve for \( x \) is:
\[ 112 + (2x + 8) = 180 \]
or simplified to the relevant steps where \( x \) can be isolated and solved.
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