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The interior angles,in degrees, of a polygon are all distinct integers

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The interior angles,in degrees, of a polygon are all distinct integers  [#permalink]

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New post Updated on: 19 Jan 2018, 07:39
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The interior angles, in degrees, of a polygon are all distinct integers. If the greatest interior angle in the polygon is 144 deg., what is the maximum number of sides that the polygon can have?
A) 5
B) 6
C) 7
D) 8
E) 9

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Originally posted by souvonik2k on 19 Jan 2018, 07:09.
Last edited by souvonik2k on 19 Jan 2018, 07:39, edited 2 times in total.
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The interior angles,in degrees, of a polygon are all distinct integers  [#permalink]

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New post 19 Jan 2018, 07:22
souvonik2k wrote:
The interior angles, in degrees, of a polygon are all distinct integers. If the greatest interior angle in the polygon is 144 deg., what is the maximum number of sides that the polygon can have?
A) 5
B) 6
C) 7
D) 8
E) 9


If the interior angles were not distinct integers
The formula for measure of interior angle of the polygon is \(\frac{(n-2)*180}{n}\)

We are given the greatest possible angle is 144 degree.
Since the angles are distinct, the angles must be at least 1 lesser than the previous angle.
The sum for 9 such angles is 140*9(144+143+142+141+140+139+138+137+136)

Hence, the equation would not be (n-2)*180 = 1260
180n = 1260+360 => n = 9(Option E)

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Re: The interior angles,in degrees, of a polygon are all distinct integers  [#permalink]

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New post 19 Jan 2018, 07:32
pushpitkc wrote:
souvonik2k wrote:
The interior angles, in degrees, of a polygon are all distinct integers. If the greatest interior angle in the polygon is 144 deg., what is the maximum number of sides that the polygon can have?
A) 5
B) 6
C) 7
D) 8
E) 9



Kindly check the answer to the question. I think it must be 10.

The formula for measure of interior angle of the polygon is \(\frac{(n-2)*180}{n}\)
We are given the greatest possible angle is 144 degree.

Hence, \(\frac{(n-2)*180}{n} = 144\)
Solving for n we will get n=10


Hi
This formula is applicable when all the interior angles are equal.
Here all angles are distinct, so this formula will not be applicable.
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The interior angles,in degrees, of a polygon are all distinct integers  [#permalink]

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New post 19 Jan 2018, 08:33
Exterior angle of the largest interior angle = 180-144 = 36 deg.
This will be the smallest exterior angle.
In order to get the largest no. of sides, let us take the exterior angles consecutive.
Sum of exterior angles of a polygon is 360 deg.
Thus, 36+37+....44=360
Maximum no. of sides = 9
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The interior angles,in degrees, of a polygon are all distinct integers  [#permalink]

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New post 19 Jan 2018, 10:02
souvonik2k wrote:
Exterior angle of the largest interior angle = 180-144 = 36 deg.
This will be the smallest exterior angle.
In order to get the largest no. of sides, let us take the exterior angles consecutive.
Sum of exterior angles of a polygon is 360 deg.
Thus, 36+37+....44=360
Maximum no. of sides = 9



I agree. I missed the part about the interior angles being different. Have corrected the solution accordingly.
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The interior angles,in degrees, of a polygon are all distinct integers &nbs [#permalink] 19 Jan 2018, 10:02
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