How to predict the bond angle and shape of a molecule of NH3

An atom of nitrogen has 5 valence electrons in its outer shell. Each hydrogen atom in ammonia bonds to the central nitrogen atom and contributes an electron each. This means there are 8 electrons in total on the central nitrogen in ammonia. Each NH bond is a pair of electrons therefore the existence of 3 NH bonds in ammonia means that 6 of these 8 electrons are involved in bonding leaving a lone pair of electrons. These 3 bonding pairs and one lone pair of electrons arrange themselves are far apart as possible to minimise repulsion and so they arrange themselves in a tetrahedral. The angles between each bond is less that 109.5 because there is greater repulsion from the lone par - it pushes the bonds closer to one another.