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# The sum of the interior angle measures for any n-sided polygon equals

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Director
Joined: 26 Oct 2016
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GMAT 1: 770 Q51 V44
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The sum of the interior angle measures for any n-sided polygon equals  [#permalink]

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07 Mar 2017, 12:40
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Difficulty:

65% (hard)

Question Stats:

60% (02:47) correct 40% (02:24) wrong based on 100 sessions

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The sum of the interior angle measures for any n-sided polygon equals 180(n – 2). If Polygon A has interior angle measures that correspond to a set of consecutive integers, and if the median angle measure for Polygon A is 140°, what is the smallest angle measure in the polygon?

(A) 130°
(B) 135°
(C) 136°
(D) 138°
(E) 140°

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Anaira Mitch

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The sum of the interior angle measures for any n-sided polygon equals  [#permalink]

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07 Mar 2017, 13:02
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anairamitch1804 wrote:
The sum of the interior angle measures for any n-sided polygon equals 180(n – 2). If Polygon A has interior angle measures that correspond to a set of consecutive integers, and if the median angle measure for Polygon A is 140°, what is the smallest angle measure in the polygon?

(A) 130°
(B) 135°
(C) 136°
(D) 138°
(E) 140°

140n=180(n-2)
n=9
smallest interior angle=140°-4°=136°
C
Director
Joined: 26 Oct 2016
Posts: 637
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GMAT 1: 770 Q51 V44
GPA: 4
WE: Education (Education)
Re: The sum of the interior angle measures for any n-sided polygon equals  [#permalink]

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15 Mar 2017, 10:43
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Posting OE of this problem.
Attachments

official_polygon.PNG [ 96.71 KiB | Viewed 1468 times ]

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Anaira Mitch

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Re: The sum of the interior angle measures for any n-sided polygon equals  [#permalink]

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21 Mar 2017, 05:13
1
anairamitch1804 wrote:
The sum of the interior angle measures for any n-sided polygon equals 180(n – 2). If Polygon A has interior angle measures that correspond to a set of consecutive integers, and if the median angle measure for Polygon A is 140°, what is the smallest angle measure in the polygon?

(A) 130°
(B) 135°
(C) 136°
(D) 138°
(E) 140°

We need to first determine the number of sides (or angles) of polygon A. Let n denote the number of sides of polygon n. Since the interior angle measures correspond to consecutive integers, the median angle measure is also the average angle measure. Since sum = average x quantity, we have sum = 140n. Since we are also given that the sum of the interior angle measures equals 180(n - 2), it must be true that 140n = 180(n - 2). Thus:

140n = 180(n - 2)

140n = 180n - 360

-40n = -360

n = 9

We now know polygon A is a 9-sided polygon and there must be 4 angles that have measures less than the median angle measure (and 4 angles that have measures greater than the median angle measure). Since the median angle measure is 140 degrees and the angle measures are consecutive integers, the smallest angle measure must be 140 - 4 = 136 degrees.

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Re: The sum of the interior angle measures for any n-sided polygon equals  [#permalink]

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12 Apr 2018, 06:20
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: The sum of the interior angle measures for any n-sided polygon equals &nbs [#permalink] 12 Apr 2018, 06:20
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