Question

He ___ over the map, searching for his destination.

Answer 1

he (looked) over the map.

Answer 2

The correct answer for this question is “looked”. He _looked__ over the map, searching for his destination.

This sentence is in continuous tense.

But the sentences show the action takes place from the past.

So the verb of this sentence should be past tense.  

This sentence explains that he searched the map for his aim.