the sum of the internal angles of a triangle are equal to 180 degrees.
once i remembered that the problem became a lot easier.
let a, b, and c be the angles of the triangle.
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let a = 2*b
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let c = a+b-12
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the above two statements are given.
since the sum of the internal angles of a triangle are equal to 180, then we have a third equation to work with which is
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a + b + c = 180
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we now have 3 equations for 3 unknowns and we should be able to solve for each of the unknowns.
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it looks like the easiest thing is to solve for b. once we find b, the rest should fall into place very nicely.
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since a = 2*b, we can substitute 2*b for a in the equation a + b + c = 180.
that equation then becomes 2*b + b + c = 180 which becomes 3*b + c = 180.
looking at the equation c = a + b - 12, we solve for b as follows:
since we know that a = 2 * b, we can substitute 2*b for a and the equation becomes c = 2*b + b - 12 which becomes c = 3*b - 12.
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the equation we are working with is 3*b + c = 180 which originally started as a + b + c = 180.
we can substitute 3*b - 12 for c and the equation becomes
3*b + 3*b - 12 = 180 which becomes 6*b = 192 after adding 12 to both sides and combining like terms.
dividing both sides of the equation by 6 and we get b = 32 degrees.
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we have b = 32 degrees.
we have a = 2 * b so a = 64 degrees.
we have c = a + b - 12 which becomes c = 32 + 64 - 12 which becomes c = 96 - 12 which becomes c = 84 degrees.
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substituting in the equation a + b + c = 180, we get 32 + 64 + 84 = 180 which becomes 96 + 84 = 180 which becomes 180 = 180.
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answer is:
a
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