如图,∠AOB=35°40′,∠BOC=50°30′,∠DOC=21°18′,OE平分∠AOD,求∠BOE的度数.

问题描述:

如图,∠AOB=35°40′,∠BOC=50°30′,∠DOC=21°18′,OE平分∠AOD,求∠BOE的度数.

∠AOD=∠AOB+∠BOC+∠COD=35°40'+50°30'+21°18'=107°28',
根据OE平分∠AOD,∠AOE=

1
2
∠AOD=53°44′,
∴∠BOE=∠AOE-∠AOB=53°44'-35°40'=18°4'.