如图,△ABC中,∠C=90°,∠ABC和∠EAC的平分线交于点D,∠ABD和∠BAD的平分线交于点F,则∠AFB的度数__

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/20 14:40:07
如图,△ABC中,∠C=90°,∠ABC和∠EAC的平分线交于点D,∠ABD和∠BAD的平分线交于点F,则∠AFB的度数__
xRj@~Pغ$3I&c^BʒlfEPRDR@ABz',T.En˾YY7W9sɸFs|?{wY)tV׼yΊ[~9>jg|b V$X]ʊM%A.>-z/*SܽOQ]uɤ @E'J%I>Px<ʋ4,M[3Bi*v< !alb h:L3L 4$)6QlfPZ(vBpB!Tmd隁HS(+eAfZf1SB,Sl lSˤ$1b.Pnj[jN&RDj~|מ|}8WbMv!~!itRD&9-D=DOBw'Fj@)z,ELJJƓKB@RV" n?vp6J۲.=\P

如图,△ABC中,∠C=90°,∠ABC和∠EAC的平分线交于点D,∠ABD和∠BAD的平分线交于点F,则∠AFB的度数__
如图,△ABC中,∠C=90°,∠ABC和∠EAC的平分线交于点D,∠ABD和∠BAD的平分线交于点F,则∠AFB的度数__

如图,△ABC中,∠C=90°,∠ABC和∠EAC的平分线交于点D,∠ABD和∠BAD的平分线交于点F,则∠AFB的度数__
∠ABD和∠BAD的平分线交于点F,则∠AFB的度数_112.5°_.
∵∠EAC-∠ABC=90° 【=∠ACB】
∴(∠EAC)/2-(∠ABC)/2=90°/2=45°
又 ∠CAB=90°-∠ABC
∴ ∠AFB=∠EAF-∠ABF
=(∠EAD+∠DAF)-(∠ABC)/4
=[(∠EAC)/2+(∠DAC+∠CAB)/2]-(∠ABC)/4
={(∠EAC)/2+[(∠EAC)/2+(90°-∠ABC)]/2}-(∠ABC)/4
=∠EAC/2+∠EAC/4+45°-∠ABC/2-∠ABC/4
=45°+3(∠EAC-∠ABC)/4
=45°+(3/4)*90°
=45°+67.5°
=112.5°