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Question 1054267: the square of the complement of an angle is equal to 90 more than three times the supplement of the angle. what is the measure of the angle
Found 3 solutions by Boreal, stanbon, MathTherapy:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! x is angle
90-x is complement
180-x is the supplement
(90-x)^2-90=3(180-x)
8100-180x+x^2-90=540-3x
x^2-177x+7470=0
x=(1/2)(177+/- sqrt (177^2-29880); sqrt term=38.07
x=(1/2)(177+/-38.07)
x=107.58, has no complement
x=69.467 angle, complement is 20.533, complement squared is 421.599, supplement is 110.533, multiplied by 3 is 331.599, subtract 90 from 421.599 and get 331.599.
The angle is 69.47 degrees.
Check: 70 should be close
complement is 20, supplement 110
complement squared is 400, but that is 70 more than 3 times the supplement.
Try 69
Complement is 21, supplement is 111
square of complement is 441, 3 times supplement is 333, and that is 108 less than the complement.
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! the square of the complement of an angle is equal to 90 more than three times the supplement of the angle. what is the measure of the angle
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Angle:: 90-x
Complement:: x
Supplement:: 180-(90-x) = 90+x
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x^2 = 3(90+x)
x^2 - 3x - 270 = 0
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x = 18
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Ans:: Angle = 90-x = 72 degrees
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Cheers,
Stan H.
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Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
the square of the complement of an angle is equal to 90 more than three times the supplement of the angle. what is the measure of the angle
Angle: 
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