I used a set of compasses and drew out the first few cases

N Subtending Angle Fraction Of Circumference = arc length = angle* (R = 1/2pi)

2 2pi 1 = 4/2N

3 5pi/3 5/6 = 5/2N

4 3pi/2 3/4 = 6/2N

5 did not draw because the 5 was too much of a bother

6 4pi/3 2/3 = 8/2N

.

N (N+2)/2N

Total arc = (N+2)/2N * 1 *N = (N+2)/2

(N+2)/2 = 60

N = 118

I used a set of compasses and drew out the first few cases

N Subtending Angle Fraction Of Circumference = arc length = angle* (R = 1/2pi)

2 2pi 1 = 4/2N

3 5pi/3 5/6 = 5/2N

4 3pi/2 3/4 = 6/2N

5 did not draw because the 5 was too much of a bother

6 4pi/3 2/3 = 8/2N

.

.

N (N+2)/2N

Total arc = (N+2)/2N * 1 *N = (N+2)/2

(N+2)/2 = 60

N = 118