To solve the equation \( (5x - 25)^\circ + 55^\circ = 180^\circ \), we can follow these steps:
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Combine like terms: \[ 5x - 25 + 55 = 180 \]
This simplifies to: \[ 5x + 30 = 180 \]
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Isolate \(5x\): \[ 5x = 180 - 30 \] \[ 5x = 150 \]
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Solve for \(x\): \[ x = \frac{150}{5} \] \[ x = 30 \]
Therefore, the solution is \( x = 30 \).