It depends on the irregular figure.
A rectangle, for example, has two.
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An irregular 7 sided heptagon normally has no lines of symmetry depending how it is constructed.
It depends on the nature of the irregularities. If you have an octagon where each alternate side is equal then you can have 8 lines of symmetry.
Rotational symmetry refers to symmetry of the figure when it is rotated about a single point in the same plane. Lines of symmetry apply to reflections. You do not have lines of rotational symmetry.
It can certainly have 0, 1, 2 or 6 lines of symmetry.
Yes. A circle has infinitely many lines of symmetry and it also has rotational symmetry of infinite order.