Let's use tetrahedral as an example. For a typical tetrahedral shaped molecules, the bond angle between all 4 atoms is 109.5o. Now instead of having all 4 atoms, one of them is replace by a lone pair, making the shape now trigonal pyramidal. Imagine the repulsion of the lone pairs on the other 3 atoms, pushing them further away, making the bond angles between lone pairs and atoms more than 109.5o. And therefore, the angel between atoms become less.
