Question 1198819
.
Two sides of a regular n-gon, when extended meet at an angle 42 degrees. 
What is the least possible value of n?
~~~~~~~~~~~~~~~~~~


<pre>
The smallest angle between the sides of regular polygon is the exterior angle
of the regular polygon, which is 360/n degrees.


Any angle between other sides of the regular polygon is a multiple of this 
minimal angle, i.e. is a multiple of 360/n degrees.


Thus to find the least possible value of n, we should select least possible 
value of n sich that 42 degrees is a multiple of 360/n.


Since 42 = 6*7 and 360 = 6*60, such least possible value of n  is 60.


Thus n = 60.


<U>ANSWER</U>.  n = 60.
</pre>

Solved.