Learn Dutch: Ik vermoed dat hij boos is. - I suspect that he is angry.

The word dat (that) is a subordinating conjunction. This means it introduces a dependent clause (a secondary part of the sentence that cannot stand on its own). In Dutch, these conjunctions push the conjugated verb—in this case, is—all the way to the end of their clause.

In English, I could just say 'I suspect he is angry', leaving out 'that'. Can I leave out dat in Dutch?

No, you cannot leave out dat in Dutch the way we often drop 'that' in English. If the grammar of the sentence requires dat to connect the two clauses, it is mandatory to include it.

Why does ik vermoed end in a 'd' instead of a 't' or 'dt'?

To make the ik (I) form of a verb, you use the verb stem. You usually get the stem by dropping -en from the infinitive. The infinitive here is vermoeden (to suspect). Dropping -en leaves vermoed. Because it is the ik form, you never add an extra 't'.

Does vermoeden always mean 'to suspect' in a negative way, like in a crime?

Not necessarily! While it can be used for police suspects, vermoeden is also commonly used in everyday speech to simply mean 'to presume', 'to guess', or 'to have a hunch' about something normal, like guessing someone is angry.