Question 167656
let the angles of the triangle be a, b, and c.
let a = 2*b
let a = c-5
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if a = 2*b, then b = a/2
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if a = c-5, then c = a+5
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since the sum of the interior angles of a triangle = 180 degrees, then
a + b + c = 180
substituting a/2 for b, and a+5 for c, we get:
a + a/2 + a + 5 = 180
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combining like terms, we get:
2*a + a/2 + 5 = 180
subtracting 5 from both side of the equation we get:
2*a + a/2 = 175
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since 2*a is the same as 4*a/2, we can substitute to get:
4*a/2 + a/2 = 175
since the denominators on the left hand side of the equation are the same, this equation becomes:
(4*a + a)/2 = 175
which becomes:
(5*a)/2 = 175
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multiplying both sides of the equation by 2 gets:
5*a = 350
dividing both sides of the equation by 5 gets:
a = 70
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a = 70
b = a/2 = 35
c = a+5 = 75
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70 + 35 + 75 = 180
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algebraic expression to solve the problem was derived above.
it started off as
a+b+c = 180
we solved for b in terms of a.
we solved for c in terms of a.
equation became:
a + (a/2) + (a+5) = 180
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the rest was simplification to come up with a = 70.
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