Question 757099: The measure of an angle is five times the measure of its supplement. Find the original angle. Found 2 solutions by Alan3354, DrBeeee:Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! The measure of an angle is five times the measure of its supplement. Find the original angle.
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Angle + (Angle/5) = 180
You can put this solution on YOUR website! Let x = the measure, in degrees, of the angle we are trying to find.
Let y = the supplement of x, in degrees
Knowing that supplementary angles add up to 180 degrees, we have
(1) x + y = 180 or
(2) y = 180 - x
Now the problem statement tells us that
(3) x = 5*y
Substituting (2) into (3) gives us
(4) x = 5*(180 - x) or
(5) x = 900 - 5*x or
(6) 6*x = 900 or
(7) x = 150
Then using (1) we get
(8) y = 180 - 150 or
(9) y = 30
Let's check this using (3).
Is (150 = 5*30)?
Is (150 = 150)? Yes
Answer: The original angle is 150 degrees.
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