Which responsibility does the legislature in a parliamentary democracy usually have? question 1 options: appointing the monarch interpreting the meaning of laws electing the head of government determining the constitutionality of laws

The correct answer is the third option.
It is the duty of the parliament in some parliamentary democracies to choose that is elect the head of the government.  For example in Sweden, the Speaker of the The Parliament proposes the candidate for the Prime Minister and he becomes a Prime Minister only if the absolute majority of the parliament approves the nomination.