If something engages you or your attention or interest, it keeps you interested in it and thinking about it. They never learned skills to engage the attention of the others
engage for service under a term of contract; "We took an apartment on a quiet street"; "Let's rent a car"; "Shall we take a guide in Rome?"
When a military force engages the enemy, it attacks them and starts a battle. It could engage the enemy beyond the range of hostile torpedoes. see also engaged, engaging
A controller being able to share data and facilities in asaid to be engaged in the collaboration area, and the collaborationto engage the controller