Select all angle measures for which cos 0=1/2

The general solution to cos(theta) = 1/2 is 2k π ± π /3, translated to degrees, the solution is
360k ± 60 degrees, where k is an integer.

For k=0, we have solutions 0 ± 60, or  {-60, +60}
For k=1, we have solutions 360 ± 60, or  {300, 420}
For k=2, we have solutions 720 ± 60, or  {660, 780}

This is sufficient to cover the range of the answer choices, giving the angle measures for which cos(theta)=1/2 as {-60,660}