Hello from MrBillDoesMath! 
 
Answer: 
120 degrees
 
Discussion: 
 The circumference of the circle is 6 and an arc of 17/3. The remaining piece of the circumference (corresponding to the central angle) is
6 - 17/3 => 6 = 18/3
 = 18/3 - 17/3
 = 1/3
As a circle has 360 degrees, (1/3) 360 = 120 degrees if the central angle.
Thank you, 
 
MrB