Lug angles are commonly used in structural connections to provide additional support and reduce the length of the connection. They are typically L-shaped and are attached to a structural member to enhance its strength and stability. Lug angles are often used in conjunction with bolts or welds to create a secure connection.

The correct answer to the given question is option 'A' - lug angles are used to reduce the length of connection. Here is a detailed explanation of why this answer is correct:

1. Purpose of Lug Angles:
- Lug angles are primarily used to provide additional support to a structural member, such as a beam or column, at its connection points.
- They help distribute the load and reduce the stresses on the connection by transferring the forces to a larger area.
- By increasing the effective length of the connection, lug angles reduce the need for longer beams or columns, thereby saving on material and construction costs.

2. Length Reduction:
- Lug angles are designed to extend beyond the end of the connected member, allowing for a shorter overall connection length.
- By extending the connection point, the effective length of the beam or column is increased, reducing the bending moment and shear forces at the connection.
- This results in a more efficient and economical design, as shorter members are generally less expensive and easier to handle during construction.

3. Unequal Angles and Shear Lag:
- The given options 'B' and 'C' - "lug angles are unequal angles" and "lug angles increase shear lag" - are incorrect.
- Lug angles can be either equal or unequal, depending on the specific design requirements and load conditions.
- Shear lag refers to the uneven distribution of forces across a connection due to the deformation or flexibility of the connected members. While lug angles can help mitigate shear lag to some extent, it is not their primary purpose.

In conclusion, lug angles are primarily used to reduce the length of a connection in structural applications. They provide additional support, distribute the load, and help optimize the design of beams or columns. While they can have other effects such as mitigating shear lag, their main purpose is to reduce the length of the connection.