(Polar molecules, Non-polar molecules, etc.)
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Just look at the electron arrangement for the atom and assume that it will be slightly less than the bond angles for that particular arrangement. For example, water has a bent shape but it's electron arrangement is tetrahedral. Therefore, we would assume that it's slightly less than 109.5.
Regions of electron density does have to do with bond angles. Some are easier to solve, like linear is 360 divided by 2 regions = 180 and tetrahedral is 360 divided by 3 regions = 120. However, others are not as easy like 109.5 (tetrahedral) and 106 (trigonal pyramidal). These angles differ because you need to maximize the distance between the atoms and reduce the repulsion. Therefore, atoms can be pulled away from lone pairs and much lower than the central atom, even if it means the other atoms are closer together.
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