The correct answer is:
Tommy and Rachel were happily eng engaged: Promised to another to be married.
The students were engaged in the scientist’s presentation: busy or interested sentence.
These engaged definitions show two cases with different meanings. Being engaged means to be occupied, involved or attracked in any situation. But the correct application depends on the context. In the case of Tommy and Rachel, they are “engaged” because they have the commitment to get married. Both have accepted an agreed. In the case of the students, they are interested and engaged or “committed” to finish the scientist’s presentation.