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PS from Yahoo Groups

by f2001290 » Thu May 24, 2007 10:40 pm
If a regular convex polygon has 'n' sides, then how many different values can 'n' take for which the interior angle of the polygon will be an integer?

A. 16
B. 18
C. 36
D. 24
E. 22

OA after few explanations
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Re: PS from Yahoo Groups

by gabriel » Thu May 24, 2007 11:19 pm
f2001290 wrote:If a regular convex polygon has 'n' sides, then how many different values can 'n' take for which the interior angle of the polygon will be an integer?

A. 16
B. 18
C. 36
D. 24
E. 22

OA after few explanations
the xterior angle of any polygon is given by 360/n ... and the interior angle is given by 180-360/n ....

... now the number of divisors of 360 are 24 .. but out of these divisors we shuld not consider 1,2 bcoz the interior angles wuld be -180 and 0 respectively ... so the number of values n can take is 24-2 = 22 .. so the answer shuld be E ..
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by Cybermusings » Fri May 25, 2007 4:46 am
If a regular convex polygon has 'n' sides, then how many different values can 'n' take for which the interior angle of the polygon will be an integer?

A. 16
B. 18
C. 36
D. 24
E. 22

Sum of interior angles of any polygon = (2n-4)*90
Each angle of a regular polygon = [(2n-4)*90]/n
= (180n - 360)/n
= 180 - 360/n
Hence find out the total number of factors of 360
Total factors of 360 = 24
However, 1 and 2 are out...since they won't make a polygon (we need minimum 3 sides)

Hence 22
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