= Solution
The relevant chelate rings contain \b[four atoms for <dppm>, five for <dppe>, and six for <dppp>], counting the <nickel> and both <phosphorus> atoms. The one-carbon bridge in <dppm> forces a compact ring and the small <bite angle> $75.62^\circ$. A two-carbon tether accommodates a five-membered chelate closer to the preferred square-planar cis angle, giving $86.99^\circ$. The more flexible three-carbon tether can open slightly beyond $90^\circ$, giving $91.77^\circ$.
For a simplified symmetric chelate with Ni–P distance $r$ and P–P donor separation $d$,
$$
d=2r\sin(\beta/2).
$$
Increasing the accessible donor separation therefore increases the <bite angle> $\beta$. The ligand is a three-dimensional tether, so ring puckering and substituent crowding matter as well as the number of methylene groups. This geometrical explanation does not require different formal <oxidation states> or <electron> counts for the three complexes.
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