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

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

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New post 18 Jun 2019, 00:03
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Re: The interior angles, in degrees, of a polygon are all distinct integer  [#permalink]

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New post 18 Jun 2019, 04:59
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Bunuel 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


sum of interior angles; 180*(n-2)
plug in values
we see at n=9
we get 180*7 ; 1260-144; 1116 which can be divided in distinct integers of 8 other angles
IMO E
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Re: The interior angles, in degrees, of a polygon are all distinct integer  [#permalink]

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New post 21 Jun 2019, 01:41
Bunuel Please share the official solution.
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The interior angles, in degrees, of a polygon are all distinct integer  [#permalink]

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New post 21 Jun 2019, 08:05
Bunuel 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



as we know that sum of exterior angles of a polygon is equal to 360 deg

the greatest interior angle in the polygon is 144 deg and corresponding exterior angle is 180-144 = 36

so 360 - 36 = 324 deg
we need distinct integer adding to 324
other exterior angles will be larger since 144 is the greatest angle of the polygon

to have the maximum number of sides we have to take the smallest possible integer angles ( that are larger than the first one)

we could have exterior angles of 37, 38, 39, 40, 41, 42, 43, 44 ( this add up to 324)

interior angles are 144, 143, 142, 141, 140, 139, 138, 137, 136

so from here, we get maximum 9 sides of the polygon

ans E
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The interior angles, in degrees, of a polygon are all distinct integer   [#permalink] 21 Jun 2019, 08:05
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