(Polar molecules, Non-polar molecules, etc.)
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I don't think you need to know any other specific angles as long as you know the general trend. For example, I think it would be acceptable to know that a trigonal pyramidal molecule has a bond angle slightly less than 109.5 degrees if you are able to explain why.
Agreed, I think it's important to note that bond angles will be smaller than expected in species with lone pairs because the lone pair-lone pair repulsion as well as the lone pair-bond repulsion will be stronger than any bond-bond repulsion, and therefore the bonds are forced closer to one another to minimize repulsion.
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