How is bond angle of a molecule measured?
The most obvious method is single crystal xray crystallography, of course, and for simple molecules, IR and microwave spectroscopy in the gas phase can be used.
For many complex (e.g. bioorganic) molecules, this fails, but there are two (afaik) last hopes to help solve/prove structures if they don´t crystallise and the usual NMR spectroscopy with added computational chemistry is not enough.

Single molecule xray diffraction, a very new approach that can only just be done on the one most brilliant xray &quot;laser&quot; source in the world, the XFEL in Hamburg. It cost 1.2 billion euros to build, and this is the &quot;killer&quot; application it is supposed to prove feasible.

RDC (residual dipolar coupling) measurements with NMR, a very fancy method where the interesting compound is trapped in an oriented (sort of &quot;stretched&quot;) gel. If the molecules of the compound have a preferred orientation in that gel (they usually do, because very few biomolecules are spherical), you observe dipolar splittings in the spectra, which would normally be averaged out due to the free tumbling of the molecules. These couplings can be used to calculate relations between distances and angles between the magnetic field and the direct connecting line between the atoms involved.


No 2 of course relies heavily on additional input from conventional (spectroscopic) methods and computer simulations.