Electron microscopes cannot clearly depict the exact shape and structure of atoms and molecules, even though it does show a vague, cloudy image. In my AP chemistry class, I learned that the bond angle of some molecules is 109.5 degrees. How is this bond angle determined so precisely, if the bonds cannot be accurately observed through a microscope?
Answer
The positions of atoms respective to each other in a crystal lattice (solid) can be determined by X-ray crystallography. From these positions bond lengths and bond angles can also be calculated accurately.
Probably the most memorable case of solving the geometrical structure of a molecule was Franklin and Gosling's X-ray crystallography of DNA, information later used by Watson and Crick to solve the mystery of DNA's structure.
For many simple (binary) compounds molecular shapes and bond angles can also be determined theoretically (see link).
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