Question 208376
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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