engage in something—be actively involved with smth.:
- Those who are too smart to engage in politics are punished by being governed by those who are dumber.
engage with something—
1. make an effort to understand and deal with smth.:
- All religions attempt to engage with the problem of the existence of suffering in this world.
2. (of part of a machine) connect with another part of the machine:
- Make sure the gear on the roller is engaged with the gear on the support.