In the given circuit, the current I₁ is

The circuit can be simplified as follows:

Applying KCL at junction A

$\Rightarrow I_3=I_1+I_2\mathrm{.....}\left(i\right)$

Applying Kirchhoff's voltage law for the loop ABCDA,

$\begin{array}{l}-30{\mathrm{I}}_1-40{\mathrm{I}}_3+40=0\\ \Rightarrow -30{\mathrm{I}}_1-40\left({\mathrm{I}}_1+{\mathrm{I}}_2\right)+40=0\\ \Rightarrow 7{\mathrm{I}}_1+4{\mathrm{I}}_2=4.....\left(\mathrm{ii}\right)\end{array}$

Applying Kirchhoff's voltage law for the loop ADEFA,

$\begin{array}{l}-40{\mathrm{I}}_1-40{\mathrm{I}}_3+80+40=0\\ \Rightarrow -40{\mathrm{I}}_2-40\left({\mathrm{I}}_1+{\mathrm{I}}_2\right)=-120\\ \Rightarrow {\mathrm{I}}_1+2{\mathrm{I}}_2=3.....\left(\mathrm{iii}\right)\end{array}$

On solving equations (ii) and (iii), $I_1=-0.44A$