Engaged means fully occupied or having your full attention. An engaged reader really focuses on the words and maybe even jots down questions or comments in the pages' margins.
If you're busy or involved with something, you're engaged in it. A formal reply to an invitation to lunch might be, "I'm sorry, I'm otherwise engaged" — meaning you already have plans. Engaged often describes people who have committed to getting married. You can see this meaning in the word's origin, the French word engagier, meaning "to pledge."
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having ones attention or mind or energy engaged
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(of facilities such as telephones or lavatories) unavailable for use by anyone else or indicating unavailability; (`engaged' is a British term for a busy telephone line)
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(used of toothed parts or gears) interlocked and interacting
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reserved in advance
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involved in military hostilities
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built against or attached to a wall
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