Question

What is the bond angle in cumulene $C_4H_4$, of the $C = C = C$ bond and $H - C - H$ bonds?

Answer 1

A hydrocarbon with three or more cumulative (consecutive) double bonds is known as a cumulene. They're similar to allenes, but they have a longer row. Butatriene $\left( {H2C = C = C = CH2} \right),$ also known as $cumulene$ is the simplest molecule in this class. Unlike most alkanes and alkenes, cumulenes are rigid, similar to alkynes, which makes them attractive for molecular nanotechnology. Another form of rigid carbon chain is polyynes. Cumulenes are present in outer-space regions where hydrogen is scarce. Heterocumulenes are cumulenes that contain heteroatoms such as carbon suboxide.

Complete step by step answer:
The angles of the $C = C = C$ bond
They are all $AX_2$ structures since the internal carbon atoms are all directly bound to two other carbon atoms.
According to the Valence Shell Electron Pair Repulsion Theory, the bond angle in an $AX_2$ device is ${180^0}$
The angles of $H - C - H$ bonding
Each carbon atom is $AX_3$ system because it is directly bound to three other carbon atoms (C, H, and H).
According to the Valence Shell Electron Pair Repulsion Theory, the bond angle in an $AX_3$ device is ${120^0}$
So, In cumulene $C_4H_4$, the bond angle between $C = C = C$ bond is ${180^0}$ and the bond angle between $H - C - H$ is ${120^0}$.

Note:
Cumulenes are rigid due to the presence of two double bonds between the carbon atoms within. Their $sp$ hybridization produces two perpendicular $\pi$ bonds, one for each of their neighbours. The carbon chain's linear geometry is reinforced by this bonding.
Isomerism occurs in cumulenes with non-equivalent substituents on both ends. As with alkenes, cis–trans isomerism occurs when the number of consecutive double bonds is odd. As with allenes, axial chirality exists when the number of consecutive double bonds is even.