如图,已知∠AOB=90°,∠AOC为锐角,OD平分∠AOC,OE平分∠BOC.(1)求∠DOE的度数;(2)当∠AOB=m°时,∠DOE等于多少度?图片
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/18 01:18:39
![如图,已知∠AOB=90°,∠AOC为锐角,OD平分∠AOC,OE平分∠BOC.(1)求∠DOE的度数;(2)当∠AOB=m°时,∠DOE等于多少度?图片](/uploads/image/z/1051390-46-0.jpg?t=%E5%A6%82%E5%9B%BE%2C%E5%B7%B2%E7%9F%A5%E2%88%A0AOB%3D90%C2%B0%2C%E2%88%A0AOC%E4%B8%BA%E9%94%90%E8%A7%92%2COD%E5%B9%B3%E5%88%86%E2%88%A0AOC%2COE%E5%B9%B3%E5%88%86%E2%88%A0BOC.%281%29%E6%B1%82%E2%88%A0DOE%E7%9A%84%E5%BA%A6%E6%95%B0%3B%282%29%E5%BD%93%E2%88%A0AOB%3Dm%C2%B0%E6%97%B6%2C%E2%88%A0DOE%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91%E5%BA%A6%3F%E5%9B%BE%E7%89%87)
如图,已知∠AOB=90°,∠AOC为锐角,OD平分∠AOC,OE平分∠BOC.(1)求∠DOE的度数;(2)当∠AOB=m°时,∠DOE等于多少度?图片
如图,已知∠AOB=90°,∠AOC为锐角,OD平分∠AOC,OE平分∠BOC.(1)求∠DOE的度数;(2)当∠AOB=m°时,∠DOE等于多少度?
图片
如图,已知∠AOB=90°,∠AOC为锐角,OD平分∠AOC,OE平分∠BOC.(1)求∠DOE的度数;(2)当∠AOB=m°时,∠DOE等于多少度?图片
1.因为OE平分角BOC,所以角BOE=角COE,因为角BOE加角AOE=90度,所以角COE加角AOE=90度,因为OD平分角AOC,所以角AOD=角COD,所以2角AOE+2角AOD=90度,所以角DOE=45度
2.=2分之M度
(1)设∠BOE = α ∠AOD= β ∠AOE=δ ∠DOE=θ
∵∠AOC为锐角,OD平分∠AOC,OE平分∠BOC.
∴∠BOE =∠EOC= α ∠AOD=∠DOC= β
又∵∠EOC= ∠AOD + ∠DOC + ∠AOE = 2β + δ = α
∴ ∠AOB= 90° = ∠BOE+∠AOE = α + δ = 2β + 2δ
∴...
全部展开
(1)设∠BOE = α ∠AOD= β ∠AOE=δ ∠DOE=θ
∵∠AOC为锐角,OD平分∠AOC,OE平分∠BOC.
∴∠BOE =∠EOC= α ∠AOD=∠DOC= β
又∵∠EOC= ∠AOD + ∠DOC + ∠AOE = 2β + δ = α
∴ ∠AOB= 90° = ∠BOE+∠AOE = α + δ = 2β + 2δ
∴ ∠DOE= θ = β + δ = 1/2 ∠AOB = 45°
(2) 当∠AOB=m°时, ∠DOE= θ = β + δ = 1/2 ∠AOB = m°/2
收起