Which verb means to infer or make a guess based on evidence?

The verb that means to infer or make a guess based on evidence is "surmise." This term is commonly used in contexts where one draws conclusions or forms opinions based on observations or indirect evidence rather than direct proof. When someone surmises, they engage in a thoughtful process where they use available information to reach a tentative conclusion, which reflects the essence of making educated guesses.

In contrast, the other options suggest different actions that do not align with the meaning of inferring or guessing. "Ingratiate" refers to the act of trying to win favor with someone through flattery or other means, which is about relationships rather than deduction. "Inveigh" means to speak or write about something with great hostility or to protest strongly, focusing more on expression of emotions than deduction. Finally, "exclaim" involves speaking or crying out suddenly, emphasizing an emotional reaction rather than a thoughtful process of deriving conclusions from evidence.