To solve for \( x \), we first need to establish a relationship between the angles provided. It looks like you have three measures: 120 degrees, \( 4x - 8 \), and 32 degrees. We can set up an equation if we assume that these angles form a linear relationship (such as being supplementary).
Assuming that these angles are supplementary (sum to 180 degrees), we can write the equation:
\[ 120 + (4x - 8) + 32 = 180 \]
Now, let's combine and simplify the equation:
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Combine the constants: \[ 120 + 32 - 8 = 144 \]
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Substitute back into the equation: \[ 4x + 144 = 180 \]
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Now, isolate \( 4x \): \[ 4x = 180 - 144 \] \[ 4x = 36 \]
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Finally, divide by 4 to solve for \( x \): \[ x = \frac{36}{4} = 9 \]
So the value of \( x \) is 9.