Answer
$25^{\circ}C$.
Work Step by Step
The given formula is
$\Rightarrow C=\frac{5}{9}(F-32)$
Substitute $F=77^{\circ}$.
$\Rightarrow C=\frac{5}{9}(77-32)$
Simplify.
$\Rightarrow C=\frac{5}{9}(45)$
$\Rightarrow C=25$
Hence, the temperature is $25^{\circ}C$.