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Two sides of a regular n-gon, when extended meet at an angle 42 degrees.
What is the least possible value of n?
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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.
ANSWER. n = 60.
Solved.