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# The measures of the interior angles in a polygon

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The measures of the interior angles in a polygon [#permalink]

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16 Apr 2013, 13:28
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45% (medium)

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69% (02:27) correct 31% (01:40) wrong based on 35 sessions

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The measures of the interior angles in a polygon are consecutive integers. The largest angle measures 110 degrees. How many sides does this polygon have?

A) 5
B) 6
C) 7
D) 9
E) 11
[Reveal] Spoiler: OA
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Re: The measures of the interior angles in a polygon [#permalink]

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16 Apr 2013, 14:11
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The sum of the angles will be a multiple of 180°. And in a polygon number of sides = number of angles.

If the first angle is 110, the others are consecutive : $$110-1,110-2,...$$

We have to make sure that their sum is a multiple of 180°. Let's try with A:
Tot sum angles: $$110+110-1+110-2+110-3+110-4=110*5-10=540$$ multiple of 180. CORRECT
With every other option we would add one or more angles that would make the sum a "NOT" multiple of 180.
Example C) 7:$$110*7-1-2-3-4-5-6$$ without doing any math here it's easy to see that $$-(1+2+3+4+5+6)=-21$$ so their sum will not be a multiple of 180
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Re: The measures of the interior angles in a polygon [#permalink]

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17 Apr 2013, 00:35
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Expert's post
guerrero25 wrote:
The measures of the interior angles in a polygon are consecutive integers. The largest angle measures 110 degrees. How many sides does this polygon have?

A) 5
B) 6
C) 7
D) 9
E) 11

Almost the same question from MGMAT:
Quote:
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

Discussed here: the-measures-of-the-interior-angles-in-a-polygon-are-127388.html
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Re: The measures of the interior angles in a polygon   [#permalink] 17 Apr 2013, 00:35
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# The measures of the interior angles in a polygon

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