Step 1: Look at where the word comes from. To bamboozle someone is to hoodwink or cheat them by confusing their judgment.
Step 2: Rule out the options one by one. Amused describes a pleasant feeling, not trickery. Perilous describes danger, not deception. Gloomy describes a low mood, not deception.
Step 3: The word left standing, Deceived, is the only one built on the idea of being cheated or misled, which is exactly what bamboozled means.
\[\boxed{\text{Deceived}}\]