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__

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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__

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°