Given desired overshoot graphically find k from the root locus (Scilab)
First, drawing two more lines with angles 53⁰ and -53⁰ should be easy, just do another plot while keeping the root locus. The lines should be,
$$ y = \tan(53^\circ)x$$ and, $$ y = -\tan(53^\circ)x.$$

Once you have those lines, set some \$k\$ to be the maximum value of the evans function and change that value until you find the one that lies on the line you plotted. I would use a binary search to pick the values of \$k\$.

s=%s;
num=2;
den=s*(s+2)
t=syslin('c',num/den);
clf;

//test your k by changing this
k = 100;

evans(t,k);
mtlb_axis([-10 10 -2 2]);

//draw the 53 deg line
r = linspace(0,-3,10);
up_line = tan(53*%pi/180)*r;
dn_line = -tan(53*%pi/180)*r;
plot(r,[up_line; dn_line],'r-.')

//pzmap of the system with feedback
figure
plzr(1/.(t*k))

//draw the 53 deg line
r = linspace(0,-3,10);
up_line = tan(53*%pi/180)*r;
dn_line = -tan(53*%pi/180)*r;
plot(r,[up_line; dn_line],'r-.')