Question 167656: In a certain triangle the measure of one angle is double the measure of a second angle, but is five degress less than the measure of the third angle. If the sum of the measures of the 3 interior angles is always 180 form an algebraic equation to express the problem?
I came up with a+2a-5=180, but this just doesn't seem right to me, could you please help? Thank you.
Found 2 solutions by gonzo, partygirl1122:
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! 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
-----
the rest was simplification to come up with a = 70.
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Answer by partygirl1122(6) (Show Source):
You can put this solution on YOUR website! let the angles of the triangle be k, m, and r.
let k = 2*m
let k = c-r
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if k = 2*m, then m = k/2
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if k = r-5, then r = k+5
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since the sum of the interior angles of a triangle = 180 degrees, then
k + m + r = 180
substituting k/2 for m, and k+5 for r, we get:
k + k/2 + k + 5 = 180
-----
combining like terms, we get:
2*k + k/2 + 5 = 180
subtracting 5 from both side of the equation we get:
2*k + k/2 = 175
-----
since 2*k is the same as 4*k/2, we can substitute to get:
4*k/2 + k/2 = 175
since the denominators on the left hand side of the equation are the same, this equation becomes:
(4*k + k)/2 = 175
which becomes:
(5*k)/2 = 175
-----
multiplying both sides of the equation by 2 gets:
5*k = 350
dividing both sides of the equation by 5 gets:
k = 70
-----
k = 70
m = k/2 = 35
r = k+5 = 75
-----
70 + 35 + 75 = 180
-----
algebraic expression to solve the problem was derived above.
it started off as
k+m+r = 180
we solved for m in terms of k.
we solved for r in terms of k.
equation became:
k + (k/2) + (k+5) = 180
-----
the rest was simplification to come up with k = 70.
-----
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