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# If d = 2c and e = a/2, what is x in terms of a, b, and c?

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Math Expert
Joined: 02 Sep 2009
Posts: 51302
If d = 2c and e = a/2, what is x in terms of a, b, and c?  [#permalink]

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19 Aug 2018, 08:53
00:00

Difficulty:

45% (medium)

Question Stats:

73% (02:24) correct 27% (02:17) wrong based on 43 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) $$540 - \frac{1}{2}a - b - \frac{3}{2}c$$

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Capture.PNG [ 64.12 KiB | Viewed 471 times ]

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Re: If d = 2c and e = a/2, what is x in terms of a, b, and c?  [#permalink]

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19 Aug 2018, 09:02
1
Bunuel wrote:

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) $$540 - \frac{1}{2}a - b - \frac{3}{2}c$$

Attachment:
Capture.PNG

sum of internal angles of a polygon = (n-2)*180
n= 6
sum of angles = 720
now,
720=a+b+c+d+e+(180-x)
x=a+b+c+d+e-540

there is only one option with a -540 (a)
still
substituting the values
x=$$\frac{3}{2}a + b + 3c - 540$$
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Re: If d = 2c and e = a/2, what is x in terms of a, b, and c?  [#permalink]

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19 Aug 2018, 09:10
Bunuel wrote:

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) $$540 - \frac{1}{2}a - b - \frac{3}{2}c$$

Attachment:
Capture.PNG

Given, $$d = 2c$$ and $$e = \frac{1}{2}a$$

Sum of the interior angles of a polygon=(n-2)*180=(6-2)*180=720

We have, a+b+c+d+e+180-x=720
Or, a+b+c+d+e-x=720-180=540
Or, x=a+b+c+d+e-540.

Substituting the value of d and e,
$$x=a+b+c+2c+\frac{a}{2}-540$$
Or, $$x=\frac{3a}{2}+b+3c-540$$

Ans. (A)
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Re: If d = 2c and e = a/2, what is x in terms of a, b, and c? &nbs [#permalink] 19 Aug 2018, 09:10
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