Explanation:

- Sagacious means having or showing keen mental discernment and good judgment; wise or shrewd.

- Option 1: Prudent

- Prudent means acting with or showing care and thought for the future.

- It is quite similar to sagacious, involving wisdom and cautiousness.

- Option 2: Ingenious

- Ingenious means clever, original, and inventive.

- It does not convey a lack of wisdom but rather creativity.

- Option 3: Ignorant

- Ignorant means lacking knowledge, awareness, or information.

- It is directly opposite to being wise, knowledgeable, or sagacious.

- This is the correct antonym.

- Option 4: Astute

- Astute means having or showing an ability to accurately assess situations or people for one's advantage.

- This is similar to sagacious and not an antonym.