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Both water (extH2extO ext{H}_2 ext{O}) and carbon dioxide (extCO2 ext{CO}_2) have exactly three atoms, yet extCO2 ext{CO}_2 is a rigid straight stick while extH2extO ext{H}_2 ext{O} is bent like a boomerang.
Why doesn't water flatten out, and what forces these atoms into precise three-dimensional angles?

The Repulsion Rule

The answer comes from VSEPR theory (Valence Shell Electron Pair Repulsion), which treats every cluster of valence electrons around a central atom as a cloud of negative charge.
In 1940, chemists Nevil Sidgwick and Herbert Powell realized that because like charges repel via Coulomb's law, valence electron pairs automatically push each other as far apart in 3D space as geometrically possible.
An electron domain is any region of high electron density around a central atom, counting every single bond, double bond, triple bond, or lone pair as exactly one domain.
If every electron domain were identical, calculating molecular angles would be pure geometry — but what happens when some domains are invisible lone pairs?

Electron Geometry vs. Molecular Shape

We must separate electron domain geometry (the layout of all electron regions) from molecular shape (the actual arrangement of visible bonded atoms).
A lone pair is an unshared valence electron pair that belongs only to the central atom, spreading out wider and exerting stronger electrostatic repulsion than a confined bonding pair.
Because repulsion strength follows extlonepair−extlonepair>extlonepair−extbondingpair>extbondingpair−extbondingpair ext{lone pair}- ext{lone pair} > ext{lone pair}- ext{bonding pair} > ext{bonding pair}- ext{bonding pair}, lone pairs squeeze adjacent bonding pairs closer together.