Question 37568
Two ways to do this one (at least).  The interior angle of any regular polygon is found by
x = (180)(N - 2) / N  where N = number of sides.  Here that is 6, so
x = 180(4) / 6 = 120 degrees.
Another way is recognizing that an inscribed angle is equal to half the number of degrees it cuts off.  The angle cuts off 4/6 of the circle...4/6 of 360 degrees is 240 degrees and half of that is 120 degrees.

Either way its's 120 degrees.