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The correct answer to this open question is the following.

Although there are no options attached we can answer the following.

One way in which Enlightenment ideas influenced political ideologies in Latin America, Asia, or Africa in the period circa 1800–2000 was the following.

Enlightenment indeed those region's political and independence movements in the creation of a form of government based on three different branches to operate the federal government.

This idea was developed by the brilliant thinker and philosopher of the Enlightenment, Baron de Montesquiou, and established a form of the executive branch, a legislative branch, and a judicial branch. Montesquiou believed that the division of powers in the federal government was the best model to rule a modern nation.

This model was first adopted by the founding fathers of the United States, and later in México, and other Latin American countries after getting their independence from the Spanish crown.