Question 1105956: two angles are supplementary. If one angle is doubled, the result is 69% less than the other angle. Find the angles
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x = the first angle
let y = the second angle.
if the angles are supplementary, their sum is 180 degrees.
x + y = 180
if one angle is doubled, the result is 69% less than the other angle.
let x be the angle that's doubled.
let y be the angle that is 69% less.
2x = y - .69y
simplify this to get 2x = .31y.
you have 2 equations that need to be solved simultaneously.
they are:
x + y = 180
2x = .31y
rearrange the second equation to get 2x - .31y = 0
your two equations are now:
x + y = 180
2x - .31y = 0
multiply both sides of the first equation by 2 and leave the second equation as is to get:
2x + 2y = 360
2x - .31y = 0
subtract the second equation from the first to get:
2.31y = 360
solve for y to get y = 360 / 2.31 = 155.8441558 degrees.
since x + y = 180, then x = 180 - y = 24.15584416 degrees.
2x = 48.31168831 degrees.
y - .69y = 48.31168831 degrees.
looks like the problem is solved.
the angles are 155.8441558 and 24.15584416 degrees.
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