Question

如图，直线AB与CD相交于点O,OE⊥AB,垂足为0，OF平分∠AOD,如果∠AOC=27°20′，试求∠COE和∠AOF的度数

如图，直线AB与CD相交于点O,OE⊥AB,垂足为0，OF平分∠AOD,如果∠AOC=27°20′，试求∠COE和∠AOF的度数

Answer 1

∵OE⊥AB
∴∠AOE=90°
∴∠COE=∠AOE-∠AOC=90°-27°20′=62°40′
∵OF平分∠AOD
∴∠AOF=∠FOD=1/2∠AOD
∵∠AOD=180°-∠AOC=152°40′
∴∠AOF=1/2∠AOD=76°20′

Answer 2

∵OE⊥AB ∠AOC＝27°20′
∴∠COE＝90°—27°20′＝62°40′
∠ AOD＝180°—27°20′＝152°40′
∵ OF平分∠AOD
∴∠AOF＝152°40′÷2＝76°20′

Answer 3

如图，直线AB与CD相交于点O,OE⊥AB,垂足为0，OF平分∠AOD,如果∠AOC=27°20′，试求∠COE和∠AOF的度数

答：根据题意可知∠COE=∠AOE-∠AOC=90°- 27°20′=62°40′
∠AOF=∠AOD×1/2 =∠COB×1/2 = （90°+62°40′）×1/2 =76°20′