如图,已知oe平分角bod.oc平分角aod,角aob等于78度,求角coe的度数.

如图,已知oe平分角bod.oc平分角aod,角aob等于78度,求角coe的度数.
如图,已知oe平分角bod.oc平分角aod,角aob等于78度,求角coe的度数.

如图,已知oe平分角bod.oc平分角aod,角aob等于78度,求角coe的度数.
∵OE平分∠BOD
∴∠DOE=1/2∠BOD
∵OC平分∠AOD
∴∠COD=1/2∠AOD
∴∠COE=1/2(∠AOD+∠BOD)=1/2*78=39°

∠COE=39°
∵OC平分∠AOD ∴∠AOC=∠COD=½*∠AOD
∵OE平分∠BOD ∴∠BOE=∠DOE=½*∠BOD
∠AOD+∠BOD=∠AOB=78°
故∠COE=∠COD+∠DOE
=½*∠AOD+½*∠BOD
=½*(∠AOD+∠BOD)=39°