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

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(75887) (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.
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