They have equal magnitudes and opposite signs.
The answer is simple, although perhaps not very satisfactory: they just do.We can make no more basic statement than this: protons (actually, their quarks) and electrons possess a quantity we call...
Protons have a charge of +1 and electrons -1 Do you need more detail?
Proton +1 neutron 0 Electron -1 I think...
A proton has a positive charge of 1.6x10 (To the power of) -19 while the electron has a negative charge of -1.6 x 10 (To the power of) -19.