Number of sigma bonds in ${\mathrm{P}}_4{\mathrm{O}}_{10}$ is:

Each phosphorus is connected to three additional oxygen atoms by a single bond, as can be shown. Thus, the total number of phosphorus-oxygen sigma bonds is,

$$\begin{gathered} =4\times 4 \\ =16 \end{gathered}$$

Each phosphorus atom now has a double bond to oxygen. One of the double bonds is single, so we also need to count that. There will be four solitary phosphorous-oxygen bonds, often known as sigma bonds.

Hence, there are 16 σ bonds in Phosphorus pentoxide