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Eight of them.
Technically no because 360/7 is a repeating decimal but it can be approximated
Divide it into 72 pieces, group them into groups of 8. DoNe
You can't. However, you can divide it into seven, like so: Make the lines make a triangle in the middle of the circle, rather than making them meet at the centre.
Select any point inside the hexagon and draw a line segment to any point on the boundary of the hexagon. Draw 7 more such segments. These will divide the hexagon into 8 parts. The parts will not be equal but that was not a requirement of the question.