Question

如图，∠AOB=125°，AO⊥OC，BO⊥OD，则∠COD=______

如图，∠AOB=125°，AO⊥OC，BO⊥OD，则∠COD=______．

Answer 1

∵AO⊥OC，BO⊥OD，
∴∠AOC+∠BOD=∠AOD+∠DOC+∠DOC+∠COB=90°+90°=180°，
∴∠COD=∠AOC+∠BOD-∠AOB=180°-125°=55°．

Answer 2

∵ao⊥oc，ob⊥od
∴角aoc=角dob=90°
∴角aod=∠aoc-∠cod=90°-38°=52°
∴∠aob=∠aod+∠dob=52°+90°
=
142°

Answer 3

设∠cod=X
∠AOD=90-X
∠BOC=90-X
∠AOB=∠AOD+∠BOC+X
125=90-X+90-X+X
解得X=55
很高兴为你解答.