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There's the normal ones like tetrahedral that you can just memorize, but for a lot of molecules where those angles are tweaked a bit you can't just memorize them other than knowing that they will be greater or less than the usual value.
I would suggest memorizing the basic angles like tetrahedral is 109.5, trigonal planar is 120, and linear is 180. Then, you should understand how lone pairs affect those angles. Lone pairs push the bonded atoms together making the angles smaller. For instance, a trigonal pyramidal is <109.5.
For a tetrahedral shape (4 areas of electron density) with no lone pairs the bond angle is 109.5 degrees, and if there is a tetrahedral shape (4 areas of electron density) with one or more lone pairs, than the bond angle is less than 109.5.
Tetrahedral is typically the angle that trips people up because it is assumed that it would be 90 degrees since there are 4 molecules, when in fact it is 109.5 degrees. All the others are fairly straightforward (ex: trigonal planar, 120, or linear, 180) or are estimated instead of exact values (ex: trigonal pyramidal, which varies but is always <109.5).
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