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# The measures of the interior angles in a polygon are

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VP
Joined: 07 Dec 2014
Posts: 1128
The measures of the interior angles in a polygon are  [#permalink]

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30 Jun 2018, 12:23
rxs0005 wrote:
The measures of the interior angles in a polygon are consecutive integers. The smallest angle measures 136 degrees. How many sides does this polygon have?

A) 8
B) 9
C) 10
D) 11
E) 13

let n=number of sides
assume that median interior angle of irregular polygon=common interior angle of regular polygon
assume that n is odd; otherwise, median angle would be non-integer
n[136°+(n-1)/2]=(n-2)(180°)
n=9
B
Director
Joined: 31 Jul 2017
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Re: The measures of the interior angles in a polygon are  [#permalink]

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30 Jun 2018, 21:05
rxs0005 wrote:
The measures of the interior angles in a polygon are consecutive integers. The smallest angle measures 136 degrees. How many sides does this polygon have?

A) 8
B) 9
C) 10
D) 11
E) 13

As the angles are consecutive.. we can write the angles as below -

$$140-4, 140-3, 140-2,140-1, 140, 140+1, 140+2, 140+3, 140+4$$. As the angles are consecutive, each angle should be an Integer.
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Re: The measures of the interior angles in a polygon are  [#permalink]

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30 Jun 2018, 21:49
I went in for Option B. This is how I approached the problem.

Sum of interior angles = (n-2)*180; where n=number of sides.
if you notice carefully, sum of interior angles always has a '0' in units digits.
Thus, the sum of these angles should also have a 0 in units digits.
You can simply add, the units digits of 136,137,138...

6+7+8+9 = 30, units digit is 0. but 4 is not there in options.
6+7+8+9+0+1+2+3+4 = 40. 9 is there in options.
6+7+8+9+0+1+2+3+4+5+6+7+9+0+1+2 = 70. 16 is not there. 13 is the largeest number of sides givin in option so no need to go on further.
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Re: The measures of the interior angles in a polygon are &nbs [#permalink] 30 Jun 2018, 21:49

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