Field
Where the atoms go
VSEPR as a repulsion minimisation rather than a table, the angles that fall out of it, and the case where five sites are not all alike.
VSEPR, computed
The tetrahedral angle is not 109.5 degrees because a textbook says so. It is arccos(−1/3), and it falls out of minimising the repulsion of four points on a sphere without ever being written down.
Five sites are not alike
Every other common arrangement has one or two distinct angles. Five has three, because two of its positions are on an axis and three are round an equator — and a molecule built that way does something about it.
Why water is bent
The standard answer is lone pair repulsion, it predicts the right direction, and it cannot predict the magnitude. A better rule can, and the heavier hydrides show where both accounts run out.