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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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Joined: 02 Sep 2009
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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, 09:53
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Question Stats:

71% (02:30) correct 29% (02:18) wrong based on 124 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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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, 10:02
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, 10:10
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?  [#permalink]

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22 Apr 2019, 08:41
Quote:
sum of internal angles of a polygon = (n-2)*180

is it applicable to all the polygons or only to regular ones?
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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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22 Apr 2019, 17:49
1
ArupRS wrote:
Quote:
sum of internal angles of a polygon = (n-2)*180

is it applicable to all the polygons or only to regular ones?

ArupRS, It is applicable for all polygons.
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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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23 Apr 2019, 20:02
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

Since the sum of the measures of the interior angles of a hexagon is 720 degrees, we can let the remaining interior angle of the hexagon = f, and create the equation:

a + b + c + d + e + f = 720

a + b + c + 2c + a/2 + f = 720

3a/2 + b + 3c + f = 720

f = 720 - 3a/2 - b - 3c

Since f and x are supplementary angles, we have:

f + x = 180

720 - 3a/2 - b - 3c + x = 180

x = 3a/2 + 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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15 Sep 2019, 20:35
a + b + c + d + e + 180-x = 720
a + b + c +2c + a/2 -x = 540
3a +2b+6c - 1080= 2x
3/2 a + b + 3c - 540 = x
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Re: If d = 2c and e = a/2, what is x in terms of a, b, and c?   [#permalink] 15 Sep 2019, 20:35
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