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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]  19 Aug 2018, 04:07
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77% (02:01) correct 22% (01:52) wrong based on 18 sessions
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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]  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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