Question 948892
{{{5pi/4-2pi=(5/4-2)pi=(5/4-8/4)pi=(-3/4)pi=highlight(-3pi/4)}}}
{{{5pi/4+2pi=(5/4+2)pi=(5/4+8/4)pi=(13/4)pi=highlight(13pi/4)}}}
There are other (infinitely many) angles,
lesser than {{{-3pi/4}}} or greater than {{{13pi/4}}} ,
that are also coterminal with {{{5pi/4}}} ,
but they are not in your list of choices because
{{{-3pi/4<pi/4<9pi/4<13pi/4}}} .
{{{drawing(300,300,-0.95,0.95,-0.95,0.95,
grid(0),arrow(0,0,-0.9,-0.9),
arc(0,0,1,1,-225,0),line(-.35,-.35,-.35,-.3),
line(-.35,-.35,-.4,-.35),locate(-0.45,-0.05,5pi/4),
red(arc(0,0,0.9,0.9,0,135)),red(line(-.32,-.32,-.27,-.32)),
red(line(-.32,-.32,-.32,-.37)),locate(0.1,-0.14,red(-3pi/4)),
green(arc(0,0,1.1,1.15,-90,0)),green(arc(0,0,1.2,1.15,-180,-90)),
green(arc(0,0,1.2,1.25,-270,-180)),green(arc(0,0,1.3,1.25,0,90))
green(arc(0,0,1.3,1.35,-90,0)),green(arc(0,0,1.4,1.35,-180,-90)),
green(arc(0,0,1.4,1.5,137,180)),locate(-.8,-.25,green(13pi/4)),
green(line(-.50,-.50,-.55,-.50)),green(line(-.50,-.50,-.50,-.45))
)}}}