Bong Angles of Cyclic Hydrocarbons

[QuantumChemist]

We're going over the reactivity of aromatic compounds so I was reviewing material over Sn1 and Sn2 reactions. In the book that we have, it says that the smaller the bong length between two carbons, or other atom, in a cyclic compound, the smaller the bond angle.

That's where I get confused. Using similar triangles, we can see that no matter how long the arms, the angle stays the same. So how is it that the smaller the bong length, the shorter the bond angle? Does the shorter length contribute to a higher steric strain or increased repulsion of electrons on the bonded atoms? Or is my geometry just really rusty?

 

[Borek]

I don't see what they mean either.

Not to mention the fact I have no idea how the bong length can influence the bond angle

 

[DrDu]

There are some effects of bond angle on bond length and strength in small rings.
The bonding in 3 and 4 membered rings is due to spx hybrids with x being larger in smaller rings, while the bonding of the hydrogen atoms is due to spx with smaller x. The higher s content in the latter type of bonds makes them more acidic. But I think the bonds in the ring become potentially weaker (and longer) than those in an unstrained ring.