# SOLUTION: Can some one please help me solve this problem? The ratio of the complements of two angles is 3:2 and the ratio of their supplements is 9:8. Find the two original angles. Than

Algebra ->  -> SOLUTION: Can some one please help me solve this problem? The ratio of the complements of two angles is 3:2 and the ratio of their supplements is 9:8. Find the two original angles. Than      Log On

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 Question 106211This question is from textbook Geometry : Can some one please help me solve this problem? The ratio of the complements of two angles is 3:2 and the ratio of their supplements is 9:8. Find the two original angles. Thank you!This question is from textbook Geometry Answer by stanbon(60778)   (Show Source): You can put this solution on YOUR website!The ratio of the complements of two angles is 3:2 and the ratio of their supplements is 9:8. Find the two original angles. ---------------- Let the two angles be x and y. The complements are 90-x and 90-y The supplements are 180-x and 180-y ------------------------ EQUATIONS: 1st: (90-x)/(90-y) = 3/2 2nd: (180-x)/(180-y) = 9/8 --------------------------- Simplifying 1st you get: 2(90-x) = 3(90-y) 180-2x = 270-3y 2x-3y = -90 --------------- Simplifying 2nd you get: 8(180-x)= 9(180-y) 8*180-8x = 9*180-9y 8x-9y = -180 ---------------- Rewrite 1st and 2nd: 1st: 2x-3y = -90 2nd: 8x-9y = -180 -------------------- Multiply 1st by 4 and solve for y: 1st: 8x - 12y = -360 Subtract from 2nd to get: 3y = 180 y = 60 ---------- Substitute into 2x-3y = -90 to solve for x: 2x-3*60= -90 2x = 90 x = 45 ============= Cheers, Stan H.