To calculate the charge on two equally charged insulating balls weighing 0.1 g each, which are separated by 8.0 cm and suspended by 30 cm strings, one must consider the forces acting on the balls. The tension in the strings can be resolved into horizontal and vertical components, where the horizontal component relates to the electrostatic force of repulsion and the vertical component balances the weight of the balls. The geometry of the setup forms a triangle, allowing the use of trigonometric functions to find the angle the strings make with the horizontal. The symmetry of the problem simplifies calculations, as both balls experience identical forces. Ultimately, the charge on each ball can be determined using Coulomb's law and the derived angles.