Question

如图,已知∠AOB=100°,∠BOC为锐角,OE平分∠BOC,OF平分∠AOC,求∠EOF的度数.？

Answer 1

(1) OF平分∠AOC ==>FOC = 1/2*∠AOCOE平分∠BOC ==>EOC = 1/2*∠BOC∴ ∠EOF =∠FOC - ∠EOC =1/2*(∠AOC - ∠BOC)= 1/2*∠AOB = 1/2 *100° = 50°∴ ∠EOF 度数为50°(2) 由(1)的推导过程可知∠EOF = 1/2*∠AOB∴...,3,1.
设∠BOC=a, 则∠BOE=a/2，
∠AOF=（100+a）/2=50+a/2，
∠BOF=∠AOB-∠AOF=100-（100+a)/2= 50-a/2
∠EOF=∠BOF+∠BOE=(50-a/2)+a/2=50
2.
把1中的100改为x就可以了,2,2011-12-13 14:04 laoye20011 | 六级
(1) OF平分∠AOC ==>FOC = 1/2*∠AOC
OE平分∠BOC ==>EOC = 1/2*∠BOC
∴ ∠EOF =∠FOC - ∠EOC
=1/2*(∠AOC - ∠BOC)...,2,∵∠AOB为直角，∠AOC为锐角，OE平分∠BOC，OF平分∠AOC，∴∠EOF=90°∠AOB=二分之一∠EOF EOF为45度，它永远是AOB的一半 (1) ∠EOF=,1,(1) OF平分∠AOC ==>FOC = 1/2*∠AOC
OE平分∠BOC ==>EOC = 1/2*∠BOC
∴ ∠EOF =∠FOC - ∠EOC
=1/2*(∠AOC - ∠BOC)
= 1/2*∠AOB
...,1,设角BOE=x，角BOF=y,，因为OE平分角BOC，所以角BOC=2角BOE，OF平分角AOC，角AOF=角FOC=角BOF+角BOC，角AOB=角AOF+角BOF=2x+2y=100度，角EOF=角BOF+角BOE=x+y，角AOB=2角EOF，角EOF=50度
(2)由（1）题已证，角A0B=2角EOF,1,如图,已知∠AOB=100°,∠BOC为锐角,OE平分∠BOC,OF平分∠AOC,求∠EOF的度数.
②如果题中没有给出∠AOB的度数,其他条件均不变,则∠AOB和∠EOF有什么关系?
P.S.:②∠AOB=2∠EOF,要求详细清楚,写的好会加分