Answer
\[\underline{40{}^\circ }\]
Work Step by Step
The relation between the temperature in \[^{\circ }\text{F}\] with Celsius can be expressed as follows:
\[^{\circ }\text{C}=\frac{\left( ^{\circ }\text{F}-\text{32} \right)}{1.8}\]
Here, \[^{\circ }\text{C}\] is the temperature unit in Celsius and \[^{\circ }\text{F}\] is the temperature unit in Fahrenheit.
Let the temperature at which the Celsius scale is equal to Fahrenheit scale be \[x{}^\circ \].
Substitute \[^{\circ }\text{F}\] and \[^{\circ }\text{C}\] with \[x{}^\circ \] in the above expression:
\[\begin{align}
& \,\,\,\,\,\,\,x{}^\circ =\frac{\left( x{}^\circ -\text{32} \right)}{1.8} \\
& \Rightarrow \,1.8x{}^\circ =x{}^\circ -\text{32} \\
& \Rightarrow \,1.8x{}^\circ -x{}^\circ =\text{32} \\
& \Rightarrow \,-0.8x{}^\circ =\text{32} \\
& \Rightarrow \,x{}^\circ =-\frac{\text{32}}{0.8} \\
& \Rightarrow \,x{}^\circ =-40 \\
\end{align}\]
At $‒40^{\circ }$, Celsius and Fahrenheit will be same.
