I've attached a drawing of the circle and the 6 points.
You are supposed to know that an angle at the perimeter of a circle is half as large as the angle at the centre both subtended over the same arc.
I've marked corresponding angles with the same colour.
Now consider the angles at the centre of the circle: The black angle + the thick blue angle = 360° and the red angle + the thin blue angle = 360°. Together they have 720°. The sum of angles at the perimeter have the half of 720° thus 360°