解:连接$AC.$
$\because AE = AD,$$AC = AC,$$CE = CD,$
$\therefore \triangle ACE\cong\triangle ACD$(SSS).
$\therefore \angle D=\angle AEC = 75^{\circ}.$
$\therefore \angle BEC=180^{\circ}-75^{\circ}=105^{\circ}.$
$\because \angle ECD=\angle B+\angle BEC,$
$\therefore \angle B = 145^{\circ}-105^{\circ}=40^{\circ}$