Err... I didn't get your question.

They are different verbs, not the same (though of the same origin).

If you just wash your face it is "умываться". If you take shower or bath it is "мыться".

Edit: Ah, got it. In your example was given "умываться" as a task and "мыться" as the correct answer. Then it is an error. Sometimes native speakers can use "мыться" as a synonymous of "умываться," but it should not be in textbook exercises.