50-60 AD
Reason: Let ∠ABD be X, then ∠DBC is X (the reason is omitted).
Because DC bisects the outer corner of ACB.
So ∠ ACD = 0.5 ∠ the outer corner of ACB.
= 0.5(≈A+2X) (the outer angle of a triangle is equal to the sum of two non-adjacent inner angles)?
=0.5∠A+X
Because ∠ d =180-x-∠ ACB-0.5 ∠ a-X.
= 180 -2X-∠ACB-0.5∠A
Because ∠ ABC+∠ ACB+∠ A = 180.
So 180-2x-∠ ACB-0.5 ∠ A = 40.
180 -∠ABC-∠ACB-0.5∠A=40
180 -? 180 +0.5∠A=40
0.5∠A=40
∠A=80
(2) As shown in the figure: A, B, C, D and F are rational numbers, and the sum of three numbers on each row, column and two diagonals in the figure is equal. Try to find the value of (AB+CD+EF)÷(A+B+C+D+E+F).
As can be seen from the figure, A+B+6 = C+D+E = F+7+2 = A+D+2 = 6+D+F = A+C+F = B+D+7 = 6+1+2.
Because f+7 F+7+2 = 6+D+F d+f.
So F+9=6+D+F
9=6+D
D=3
Because D=2, A+D+2=A+3+2=A+B+6.
B=- 1
Because d = 3 and b =- 1.
So B+D+7=9.
So A+D+2 = A+3+2 = 9 and A = 4.
F+7+2=9，F=0
6+E+2=9，E= 1
C+D+E=C+3+ 1=9，C=5
(A b+ CD+EF)÷(A+b+ C+D+E+F)= 1 1/ 12
Given a+3b+c=0( 1)3a-3b-4c=0(2), find a:b:c b: c b: c.
( 1)+(2)=4A-3C=0
4A=3C
C=4/3A
Substitute C=4/3A into (2).
B=-7/9A
A: b; C=9: 12:-7
4) The length of express train is 168m, and the length of local train is 184m. If two cars drive in the opposite direction, it takes 4 seconds from meeting to leaving; If driving in the same direction, it takes 16s to catch up with the local train from the express train, so find the speed of the two cars.
Set the fast speed XM/ sec and the idle speed YM/ sec.
According to the meaning: 4(X+Y)= 168+ 184.
16(X-Y)= 168+ 184
X=55，Y=33。