The three angles of a triangular flag are x, twice the complement of x, and one-half the supplement of x. find the angle measures

Complement of x is the number that adds to x to get 90
so complement is y so
x+y=90, then solving for y
y=90-x
twice of that
so 180-2x

1/2 the supplement of x
supplement is what adds to it to get 180
let's say it is z
z+x=180
z=180-x
half of that
z/2=(180-x)/2
let's
but that other thing is bla, so
(180-x)/2

x+180-2x+(180-x)/2=180
since all angles add to 180 in a triangle
add like terms
180-x+(180-x)/2=180
180-x+90-x/2=180
270-3x/2=180
minus 270 both sides
-3x/2=-90
times  2 both sides
-3x=-180
divide bot sides by -3
x=60
complement of that is 90-60=30, but twice of that is 60

then 1/2 supplement
180-60=120, half of that is 60

all angles are 60 degrees