Solution:

Here, temperature at Fahrenheit scale (F) = -40 ºF,

the temperature at Celsius scale (C) =?

From the temperature transformation formula we have,

\(\frac{C-0}{100}=\frac{F-32}{180}\)

Or, \(\frac{C-0}{100}=\frac{-40-32}{180}\)

Or, \(C=\frac{-72}{180}\times100\)

∴ C = -40ºC

Hence -40 ºC = -40 ºF

There is no special reason for this same value in different scales. It is a mere coincidence. **Based on the definitions of the Fahrenheit scale and the Celsius scale -40**º**F = -40**º**C.**