SOLUTION: The 3 angles of a triangular flag are x, 4 times the complement of x, one-third the supplement of x. Find the angle measures

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Question 756594: The 3 angles of a triangular flag are x, 4 times the complement of x, one-third the supplement of x. Find the angle measures
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!
let angles be alpha,beta, and gamma
if we have a triangle, we know that alpha%2Bbeta%2Bgamma=180

if 3 angles of a triangular flag are alpha=x,
beta equal 4 times the complement of x, and we know that complementary angles are angles whose measures sum to 90°, then the complement of x is 90-x
so, beta=4%2890-x%29

and if gamma equal to one-third the supplement of x which is 180-x, then gamma=%281%2F3%29%28180-x%29
now substitute all in alpha%2Bbeta%2Bgamma=180
x%2B4%2890-x%29%2B%281%2F3%29%28180-x%29=180....solve for x
x%2B360-4x%2B60-x%2F3=180
420-3x-x%2F3=180...both sides multiply by 3
1260-9x-x=540
1260-10x=540
1260-540=10x
720=10x
720%2F10=x
72=x
now find angles
alpha=x => highlight%28alpha=72%29
beta=4%2890-x%29 => beta=4%2890-72%29 => highlight%28beta=72%29
gamma=%281%2F3%29%28180-x%29 => gamma=%281%2F3%29%28180-72%29 => highlight%28gamma=36%29

check the sum:
alpha%2Bbeta%2Bgamma=180
72%2B72%2B36=180
180=180