Verified answer

Solution in image.

You didn't tell us the tension in ANY of the ropes, so it's impossible to find the tensions in the "other" ropes.

But let's suppose the tension in the due-north rope is 100N.  Then you'd have

100N/sin(110) = T2/sin(150) + T3/sin(100), where T2 is the tension in the rope that extends towards 100 degrees, and T3 is the tension in the rope that extends towards 210 degrees.

Now it would just be a matter of pushing buttons!