Step 1: Concept
Hybridization is determined by the number of sigma ($\sigma$) bonds and lone pairs around an atom.
Step 2: Meaning
In ethyne ($HC \equiv CH$), each carbon atom is triple-bonded to another carbon and single-bonded to a hydrogen.
Step 3: Analysis
Each carbon in ethyne forms 2 $\sigma$ bonds (one with $H$ and one with $C$) and 2 $\pi$ bonds. A steric number of 2 corresponds to $sp$ hybridization.
Step 4: Conclusion
This results in a linear molecular geometry with a bond angle of 180$^{\circ}$.
Final Answer: (C)