Find the current in each wire applying only Kirchhoff voltage law

Explanation

Applying kirchhoff voltage law in loop ABEFA
`i_(1)+30+2(i_(1)+i_(2))-10=0`
`3i_(1)+2i_(2)+20=0` … (i)
Applying kirchhoff voltage law in BCDEB
`+30+2(i_(1)+i_(2))+50+2i_(2)=0`
`4i_(2)+2i_(1)+80=0`
`2i_(2)+i_(1)+40=0` .... (ii)
Solving (i) and (ii)
`3[-40-2i_(2)]+2i_(2)+20=0`
`-120-4i_(2)+20=0`

`i_(2)=-25A`
and `i_(1)=10A`
`thereforei_(1)+i_(2)=-15A`
current in wire AF= 10 A from A to E
current in wire 15 A from B to E
current in wire DE = 25 A from D to C