解：?$(1)$?∵?$B'N// A'M，$?∴?$∠B'NC=∠A'EC = 48°$?
又∵?$EC// MD，$?∴?$∠A'EC=∠EMD$?
∴?$∠A'MD = 48°$?
?$ (2) ①$?∵?$B'N// A'M，$?∴?$∠B'NC=∠A'EC =α$?
又∵?$EC// MD，$?∴?$∠A'EC=∠EMD=α$?
∵?$∠AMN+∠A'MN+∠EMD = 180°，$?且?$∠AMN=∠A'MN=β$?
∴?$2β+α= 180°，$?則?$β=\frac {180 - α}2$?
②∵?$∠DMN$?被?$A'M$?平分，∴?$∠A'MD=∠A'MN$?
?$ $?又由翻折的性質(zhì)得?$∠AMN=∠A'MN$?
∴?$∠A'MD+∠A'MN+∠AMN = 180°，$?即?$3∠A'MD = 180°$?
∴?$∠A'MD = 180°÷3 = 60°$?
