First let's specify all angles with respect to the x-axis and determine qualitatively the directions of travel with respect to the x and y axes. It helps to actually graph this as you go and gives you a check on your final answer!
The first direction is already measured with respect to (wrt) the x-axis so we can leave that alone.
The second direction is 50° N or W which is 40° W of N.
The third direction is already measured wrt the x-axis.
Next write the 3 directions in terms of their west i components (x-direction) and j components (y-direction).
Bold letters indicate vector notation.
X1 = 25·(cos 20° i + sin 20° j) km = (23.5 i + 8.55 j) km
x2 = 35·(-cos 40° i + sin 40° j) km = (-26.8 i + 22.5 j) km
x3 = 10·(-cos 10° i - sin 10° j) km = (-9.85 i - 1.74 j ) km
The (-) signs indicate that the directions translate into motion to the left (-x) or down (-y)
Now add all the x-components and y-components separately to get the final position.
xf = (23.5-26.8-9.85) i + (8.55+22.5-1.74) j km
= -13.2 i + 29.3 j km (final position vector)
The displacement is [(-13.2)² + (29.3)²]½ = 32 km at an angle of 66° North of West
The last comes from using the x and y-components of the final displacement vector to find tan θ