Depends on what phase sequence you adopt and the reference phase for 0 degrees. In this case the magnitudes are of greater significance. But the three currents must be a balanced set (to the extent that they balance to zero), which means both magnitude & phase must be consistent.

 

Correct answers are

\( I_a=52.92 \angle{-66.74^o} \ A \)

\( I_b=37.2 \angle{ -152.5^o} \ A\)

\( I_c=66.9 \angle{ 79.58^o} \ A \)

I see what I did wrong. I failed to include the 120 degree angle offsets between the phase currents.

So I got the following for the currents. I apparently chose a different reference than you, but the angle differences are the same as yours.

\( I_a_b=20 \angle{ 94.16^o} \ A \)

\( I_b_c=30 \angle{ 0.00^o} \ A\)

\( I_c_a=40 \angle{ -145.84^o} \ A \)

\( I_a=52.92 \angle{ 53.26^o} \ A \)

\( I_b=37.24 \angle{ -32.39^o} \ A\)

\( I_c=66.98 \angle{ -160.41^o} \ A \)

 

I see what I did wrong. I failed to include the 120 degree angle offsets between the phase currents.

So I got the following for the currents. I apparently chose a different reference than you, but the angle differences are the same as yours.

\( I_a_b=20 \angle{ 94.16^o} \ A \)

\( I_b_c=30 \angle{ 0.00^o} \ A\)

\( I_c_a=40 \angle{ -145.84^o} \ A \)

\( I_a=52.92 \angle{ 53.26^o} \ A \)

\( I_b=37.24 \angle{ -32.39^o} \ A\)

\( I_c=66.98 \angle{ -160.41^o} \ A \)

Yep - you chose the current phase for Inc. I took the line-to-line Vab as the reference.

 

I see what I did wrong. I failed to include the 120 degree angle offsets between the phase currents.

So I got the following for the currents. I apparently chose a different reference than you, but the angle differences are the same as yours.

\( I_a_b=20 \angle{ 94.16^o} \ A \)

\( I_b_c=30 \angle{ 0.00^o} \ A\)

\( I_c_a=40 \angle{ -145.84^o} \ A \)

\( I_a=52.92 \angle{ 53.26^o} \ A \)

\( I_b=37.24 \angle{ -32.39^o} \ A\)

\( I_c=66.98 \angle{ -160.41^o} \ A \)

Yep - you chose the current phase for Ibc. I took the line-to-line Vab as the reference.