Question 208376: The sum of the complement and supplement of an acute angle exceeds 20 less than thrice its complement by 60. Find the measure of the acute angle.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x = the angle.
let a = the complement of the angle
let b = the supplement of the angle
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a + b = 3*a - 20 + 60
this becomes:
a + b = 3*a + 40
subtract a from both sides to get:
b = 2*a + 40
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complement of the angle is 90 - x, so a = 90 - x
supplement of the angle is 180 - x, so b = 180 - x
substitute in the equation of b = 2*a + 40 to get:
180 - x = 2 * (90 - x) + 40
this becomes:
180 - x = 180 - 2x + 40
subtract 180 from both sides and add 2x to both sides to get:
2x - x = 40
which becomes
x = 40
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if x = 40, then a = 50 and b = 140
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equation of a + b = 3 * a + 40 becomes:
50 + 140 = 3 * 50 + 40
this becomes:
190 = 150 + 40
which becomes:
190 = 190
confirming that the value of x = 40 in the original equation is correct.
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