解：?$ (2)①$?由折疊可知?$∠AOC=∠A'OC，$?
∴?$∠AOA' = 2∠AOC，$?
由折疊知，?$∠BOD=∠B'OD，$?
∴?$∠BOB' = 2∠BOD。$?
∵點(diǎn)?$B'$?落在?$OA'$?上，
∴?$∠AOA'+∠BOB' = 180°，$?
∴?$2∠AOC + 2∠BOD = 180°，$?
∴?$∠AOC+∠BOD = 90°，$?即?$∠COD = 90°。$?
②由折疊可知，?$∠AOA' = 2∠AOC，$?
?$∠BOB' = 2∠BOD。$?
∵?$∠AOC = 44°，$??$∠BOD = 61°，$?
∴?$∠AOA' = 2∠AOC = 2×44°=88°，$?
?$∠BOB' = 2∠BOD = 2×61°=122°，$?
∴?$∠A'OB'=∠AOA'+∠BOB'-180°$?
?$=88°+122°-180°=30°。$?
