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To find out how many hours the plumber worked, you can use the formula:
\[
\text{Total charge} = \text{Hourly rate} \times \text{Number of hours}
\]
In this case, the total charge is $180 and the hourly rate is $45. Plugging these values into the formula gives:
\[
180 = 45 \times \text{Number of hours}
\]
To find the number of hours, divide both sides by $45:
\[
\text{Number of hours} = \frac{180}{45} = 4
\]
Thus, the plumber worked for **4 hours**.