Supplementary angles are two angles whose measures add up to \(180\) degrees. In this case, you have one angle represented by \((x - 7)\) degrees and the other as \(43\) degrees.
To set up the equation, we can write:
\[ (x - 7) + 43 = 180 \]
Now, let's solve for \(x\):
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Combine like terms: \[ x - 7 + 43 = 180 \] \[ x + 36 = 180 \]
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Subtract \(36\) from both sides: \[ x = 180 - 36 \] \[ x = 144 \]
So, the value of \(x\) is \(144\).
To verify, we can check the measures of both angles:
- The first angle is \(x - 7 = 144 - 7 = 137\) degrees.
- The second angle is \(43\) degrees.
Now, checking the sum: \[ 137 + 43 = 180 \]
This confirms that our solution is correct. Hence, \(x = 144\).
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