Wearing goggles or having the appearance of wearing goggles; having wide, prominent eyes like someone in goggles.
From be- + goggle (from Middle English gogelen, meaning to turn the eyes or stare). The -ed ending creates an adjective meaning 'provided with' or 'wearing goggles.'
The 'be- + noun + -ed' pattern is still alive in modern English—think of 'bearded,' 'begowned,' or 'befriended'—and 'begoggled' is a perfect example of how this old formula lets us describe people as 'equipped with' something.
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