How to calculate humidity using outside temperature and outside relative humidity?
You can easily achieve that assuming that there is no sources of water vapour inside, so the absolute humidity (mass of water per volume of air), remains constant. This excerpt from my undergrad tesis will explain the formula for absolute humidity

Once you know the absolute humidity, you can adapt the same formula to calculate the relative humidity of a parcel of outside air (of now known content of water), that is taken from outside to inside a building where its temperature risen to a new value. If we add subscripts "e" to exterior temperature and relative humidity and "i" for interior ones. Most of the constants can be dropped and the interior relative humidity would be given by