Answer
$D_{E}=-288\space units,\space D_{N}=156\space units$
Work Step by Step
We can write,
$A+B+C+D=0$ ; Where D is the unknown vector.
Let's assume the units of the vector as $p$
We can get,
$D_{E}=-(A_{E}+B_{E}+C_{E})$ ; Let's plug known values into this equation.
$D_{E}=(113\space p)cos60^{\circ}-(222\space p)cos35^{\circ}-(177\space p)cos23^{\circ}=-288 \space units$
Also,
$D_{N}=-(A_{N}+B_{N}+C_{N})$ ; Let's plug known values into this equation.
$D_{E}=(113\space p)sin60^{\circ}-(222\space p)sin35^{\circ}-(177\space p)sin23^{\circ}=-156 \space units$
