$\widehat{ACB}+\widehat{ABC}=180^o-\widehat{BAC}<180^o$
$\widehat{DEC}+\widehat{ABC}=\widehat{DEC}+\widehat{AED}=180^o$
$\Rightarrow \widehat{ACB}+\widehat{ABC}<\widehat{DEC}+\widehat{ABC}$
$\Rightarrow \widehat{ACB}<\widehat{DEC}$
$\Rightarrow DE<DC$
$\Rightarrow DB<DC$