Need help! - Geometry (Hexagon inscribed in a circle)

In the center, there are 6 angles. The sum of the measures of these 6 angles = 360º

Since each angle has the same measure, we can say 6 * measure of one of these angles = 360º

so...

the measure of one of these angles = 360º/6 = 60º

In the picture, I just added 60º to the measure every time I went another 60º.

So, when Q is rotated 240º clockwise, it will end up where U is now.

Note that each successive point is separated by 60°......so......

Going clockwise four points from G  =  4 * 60°  =  240°  gives us point U as a result