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

Question

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

shridhar786 · Accepted Answer

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

Archit3110 · Answer

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

Lampard42 · Answer

Bunuel  Please share the official solution.

testtakerstrategy · Answer

Is this a medium level question? Seemed on the hard side. How are difficulties determined on gmat club

Bunuel · Answer

The difficulty level of a question is calculated automatically based on the timer stats from the users which attempted the question. So our stats say that it's 600-700 level question.

Pooki · Answer

OA E
Total degree of internal angle left = 180*(n-2)-144= 180*n-504
now tried from the largest number of n
n=9 =>180*9-504=1014
1014/8=126...<144 => sufficent

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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