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555-605 (Medium)|   Geometry|      
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If d = 2c and e = a/2, what is x in terms of a, b, and c? 19 Aug 2018, 09:53
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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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A
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If d = 2c and e = a/2, what is x in terms of a, b, and c? 19 Aug 2018, 10:02
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Bunuel

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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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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If d = 2c and e = a/2, what is x in terms of a, b, and c? 19 Aug 2018, 10:10
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Bunuel

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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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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If d = 2c and e = a/2, what is x in terms of a, b, and c? 22 Apr 2019, 08:41
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Quote:
sum of internal angles of a polygon = (n-2)*180
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is it applicable to all the polygons or only to regular ones?
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If d = 2c and e = a/2, what is x in terms of a, b, and c? 22 Apr 2019, 17:49
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ArupRS
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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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ArupRS, It is applicable for all polygons.
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If d = 2c and e = a/2, what is x in terms of a, b, and c? 23 Apr 2019, 20:02
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Bunuel

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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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

Answer: A
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If d = 2c and e = a/2, what is x in terms of a, b, and c? 15 Sep 2019, 20:35
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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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If d = 2c and e = a/2, what is x in terms of a, b, and c? 24 Jan 2020, 03:05
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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


f + x = 180

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

x = 3a/2 + b + 3c - 540

Therefore A is correct
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If d = 2c and e = a/2, what is x in terms of a, b, and c? 06 Jun 2021, 01:23
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Given figure is Hexagon ( sides = n = 6).

Interior angles sum: (n - 2)180 = 720

=> a + b + c + d + e + f(not given) = 720

=> a + b + c + 2c + 0.5a + 180 - x = 720 [f + x = 180 as straight line angles]

=> 1.5a + b + 3c - x = 540

=> \(x = \frac{3}{2}a + b + 3c - 540\)

Answer A
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If d = 2c and e = a/2, what is x in terms of a, b, and c? 21 Feb 2025, 08:38
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