(Polar molecules, Non-polar molecules, etc.)
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The presence of lone pairs causes a higher repulsion since in terms of repulsion, lone pair---lone pair > lone pair---bonded atom > bonded atom---bonded atom, so the lone pair will take the place of a bonded atom and essentially exert greater repelling force against the other atoms, pushing them closer together (so the bonded angles will decrease).
That is correct. For instance, compounds with AX4 (tetrahedral) formula would have bond angles of 120 degrees, while AX3E (trigonal pyramidal) would have bond angles of slightly less than 120 degrees due to the lone pair.
You are correct. Lone pairs on the central atom repel against the electrons in the bonding pair. This causes the atoms attached via the bonding pair to come closer together due to the repulsion which is why the expected angle is less than normal
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