MathRevolution wrote:
[GMAT math practice question]
An inner angle of an n-regular polygon is a positive integer. How many possible ns are there less than or equal to 20?
A. 10
B. 11
C. 12
D. 13
E. 14
An inner angle of an n-regular polygon is a positive integer. How many possible ns are there less than or equal to 20?
A. 10
B. 11
C. 12
D. 13
E. 14
The sum of angles in a n-sided polygon is (n-2)*180, and so each inner angle =\(\frac{(n-2)*180}{n}\)
Now \(\frac{(n-2)*180}{n}\) will be an integer
(1) When n is a factor of 180...180=2*2*3*3*5
So n can be 3, 4, 5, 6, 9, 10, 12, 15, 18 and 20......Minimum is 3 as polygon has to have at least 3 angles---11 values
(2) Apart from we can check for the remaining number if n is a factor of (n-2)*180..
n=7......(7-2)*180=5*180....NO
n=8......(8-2)*180=6*180=8*27*5.....YES
n=11.....9*180...NO
n=13....11*180...NO
n=14....12*180..NO
Similarly 16, 17 and 19 will also give a NO as the answer
Total -10+1=11
B