1. having formally agreed to marry someone
2. busy with or involved in an activity
3. participating actively or showing interest

Examples

• They got engaged last month and plan to marry next year.
• She was engaged in reading when I called her name.
• The students were fully engaged during the science experiment.
• The phone line is engaged, please try again later.
• He remained engaged in community service throughout his retirement.
• The engaged couple announced their wedding date.
• The teacher kept the children engaged with interactive games.