AE is the bisector of the angle BAC in the triangle ABC, and the angle c is greater than the angle B. if the point F D on AE is perpendicular to B C and D, then the quantitative relationship between the angle EFD and the angle c · B is? A reward of 100 yuan is offered

AE is the bisector of the angle BAC in the triangle ABC, and the angle c is greater than the angle B. if the point F D on AE is perpendicular to B C and D, then the quantitative relationship between the angle EFD and the angle c · B is? A reward of 100 yuan is offered

Go through a as ah ⊥ BC and hand over BC to H
No matter where point F is on AE, because of FD ⊥ BC, ∠ DFE = ∠ hae, ∠ EDF = ∠ EHA = 90 degree
∠C+∠CAH=1/2∠A-∠HAE=90°
1/2∠A+∠HAE+∠B=90°,∴∠HAE=1/2(∠C-∠B)( ∵∠C>∠B)
∴∠DFE=1/2(∠C-∠B)

As shown in the figure, in the triangle ABC, AE bisects the angle ABC (angle c is greater than angle b), f is on the extension line of AE, and FD is perpendicular to BC and D. calculate the angle EFD and angle B, angle C

The expression is wrong, the question should be AE bisector BAC
∵ AE bisection ∠ BAC
∴∠BAE=(1/2)∠A=(1/2)(180°-∠B-∠C)=90°-(1/2)∠B-(1/2)∠C.
∵ FD vertical BC
∴∠F=90°-∠FED=90°-(∠B+∠BAE)=90°-[∠B+90°-(1/2)∠B-(1/2)∠C]
I.e. f = (1 / 2) (C - b)

Problem: in the triangle ABC, AE bisects ∠ BAC, f moves on AE, FD ⊥ BC on D, ∠ C > ∠ B, try to determine the relationship between ∠ EFD and ∠ B, ∠ C?
I can't draw it. Ha ha

The answer of a1377051 is to take a special value, which cannot be done because there may be another answer
FG is perpendicular to ab through F, so angle AFG = angle AFD. So angle GFE = angle DFE
Angle GFE = 360-90-angle B-angle Feb
Angle DFE = 360 - 90 - angle c - angle FEC
Because the angle Feb = 180 degrees - the angle FEC
Therefore, angle GFE = 270 degrees - angle B - (180 degrees - angle FEC)
= 90 degrees - angle B + angle FEC ＾＾＾＾＾＾＾＾＾＾＾ 1
Angle DFE = 270 degrees - angle c - angle FEC ＾＾＾＾＾＾＾＾＾＾ 2 Formula
Formula 1 + formula 2 is as follows:
2-angle DFE = 360 degrees - angle B - angle c
Therefore, the angle DFE = 180 degrees - 1 / 2 (angle B + angle c)