A two-hinged arch is a structural element that consists of two supports (hinges) at either end and a curved member (arch) in between. It is classified as a statically indeterminate structure because the equilibrium conditions alone are not sufficient to determine the internal forces and reactions in the arch. The degree of indeterminacy for a structure refers to the number of additional equations required to fully determine the internal forces and reactions.

**Understanding Statically Indeterminate Structures:**
Statically indeterminate structures are those that cannot be analyzed using only the principles of static equilibrium. The number of additional equations required to solve such structures is equal to the degree of indeterminacy. In other words, the degree of indeterminacy represents the number of unknowns that cannot be solved using the equations of equilibrium alone.

**Degree of Indeterminacy for a Two-Hinged Arch:**
In the case of a two-hinged arch, the degree of indeterminacy is 1. This means that one additional equation beyond the equations of equilibrium is needed to solve the structure completely. The reason for this indeterminacy is that the arch is able to rotate at the hinges, introducing additional unknowns into the analysis.

**Reasoning behind Option 'B':**
The correct answer to the question is option 'B' because a two-hinged arch is statically indeterminate by one degree. This means that one additional equation, beyond the equilibrium equations, is necessary to fully determine the internal forces and reactions in the arch.

**Conclusion:**
A two-hinged arch is statically indeterminate by one degree because it introduces one additional unknown into the analysis due to the rotational freedom at the hinges. The degree of indeterminacy represents the number of additional equations required to fully solve the structure. It is important to understand the concept of indeterminacy in order to correctly analyze and design statically indeterminate structures.