Assume the discover charges 30% Apr and that each month you make only minimum of payment of 2.0% of the balance

30% of the payment you get every week and 2.0%

Sector area = (central angle / 360) * PI * radius^2
40 = (central angle / 360) * PI * 10^2
40 = (central angle / 360) * 314.159265
central angle = 360* 40 / 314.159265
central angle = 14,400 / 314.159265
central angle = 45.8366236628 degrees

Source:
http://www.1728.org/radians.htm