Infinitely many.
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Infinitely many.
1
An infinite number of lines.
A sphere has an infinite number of planes of symmetry. The plane must include the center of the sphere, but it can tilt at any angle. The question is the same as asking "How many planes can be drawn through one point ?" The answer is: An infinite number. And as long as the point is the center of the sphere, each plane is a plane of symmetry of the sphere.
Given a line, there are an infinite number of different planes that it lies in.