e) Ta có: $\triangle$AIB = $\triangle$DFB (cmt)
$\Rightarrow$$\widehat{AIB}$=$\widehat{DFB}$=$180^o$-$\widehat{BFI}$=$180^o$-$60^o$=$120^o$
$\Rightarrow$$\widehat{AIB}$=$180^o$-$\widehat{AIB}$=$60^o$
$\Rightarrow$$\widehat{AID}$=$\widehat{AIB}$-$\widehat{BIF}$=$120^o$-$60^o$=$60^o$
$\Longleftrightarrow$$\widehat{AIC}$=$\widehat{AID}$
$\Longrightarrow$ IA là tia phân giác của $\widehat{DIE}$