Final answer:
The question has a possible error with duplicate options, but it seeks to find a statement that correctly describes the relationship between angles ∠ACB and ∠BDC, either as a linear pair or vertical angles. More context is needed for a definitive answer.
The correct option is not given.
Step-by-step explanation:
The question appears to be asking for the correct statement to complete a geometrical proof involving angles ∠ACB and ∠BDC. In geometry, understanding the relationships between angles is crucial, such as whether they form a linear pair or are vertical angles.
A linear pair of angles is a pair of adjacent, supplementary angles, meaning they add up to 180 degrees. Vertical angles are the angles opposite each other when two lines cross. They are called "vertical" because they share the same vertex (or corner point), not because they are in any particular direction.
Vertical angles are always equal. Due to the duplication in options 1 and 3 mentioning a linear pair, and 2 and 4 mentioning vertical angles, it seems there might be an error in the question. However, depending on the specific geometry of the angles ∠ACB and ∠BDC, only one option would be factually correct; we need more context to provide a decisive answer.
The correct option is not given.