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If d = 2c and e = a, what is x in terms of a, b, and c? (A)

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If d = 2c and e = a, what is x in terms of a, b, and c? (A) [#permalink] New post 19 Aug 2018, 04:07
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If \(d = 2c\) and \(e = \frac{1}{2}a\), what is x in terms of a, b, and c?

(A) \(\frac{3}{2}a + b + 3c - 540\)
(B) \(\frac{3}{2}a + b + 3c\)
(C) \(720 - \frac{3}{2}a - b - 3c\)
(D) \(720 - \frac{1}{2}a - b - 2c\)
(E) \(540 - \frac{1}{2}a - b - \frac{3}{2}c\)
[Reveal] Spoiler: OA

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Re: If d = 2c and e = a, what is x in terms of a, b, and c? (A) [#permalink] New post 20 Aug 2018, 05:40
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This is a six sided polygon. Among the six sides we know the five sides are given as variables. Let us suppose the sixth side is f. It follows f=180-x hence x=180-f


For six sided polygon total degrees inside the polygon is given by (n-2)180 = (6-2)180= 720

From this 720=a+b+c+d+e+f
or, 720-a-b-c-2c-1/2 a = f
replacing the value of d and e as mentioned in the question

Since x=180-f
x= 180-(720-a-b-c-2c-1/2 a)
rearranging the term we get x as option A

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Re: If d = 2c and e = a, what is x in terms of a, b, and c? (A)   [#permalink] 20 Aug 2018, 05:40
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