$解:①α+β=180°,理由如下:$
$∵∠BAC=∠DAE, ∴∠BAC-∠DAC=∠DAE-∠DAC$
$即∠BAD=∠CAE$
$在△ABD和△ACE中$
$\begin{cases}{ AB=AC }\ \\ {\ ∠BAD=∠CAE} \\{ AD=AE} \end{cases}$
$∴△ABD≌△ACE(SAS),∴∠B=∠ACE$
$∴∠B+∠ACB=∠ACE+∠ACB=∠BCE=β, ∴∠B+∠ACB=β$
$∵∠BAC+∠B+∠ACB=180°,∴α+β=180°$
$②當(dāng)點D在射線BC上時,α+β=180°;$
$當(dāng)點D在射線BC的反向延長線上時,α=β$