How could you politely end a conversation with a person who is so annoying?

You can end it without being rude by keeping it short, polite, and neutral. Here are a few ways:

Use time as an excuse
“I’d love to chat more, but I need to get back to something now. Let’s catch up another time.”

Redirect and close:
“Thanks for sharing, I’ll think about that. I’ve got to step away now, talk later.”

Set a clear boundary:
“I should stop here for now. Let’s continue another time.”

Polite but firm exit:
“I need to go now. Take care.

The key is to sound respectful, but give no opening for the person to drag the conversation on.