Final answer:
The theory that suggests industrialized nations of the West are crucial in "developing" the underdeveloped world is dependency theory, which outlines how exploitation leads to global inequality.
Step-by-step explanation:
The theory that posits that the industrialized nations of the West play a strategic role in "developing" the underdeveloped world is known as dependency theory. This perspective articulates that global inequality is largely a consequence of core nations exploiting resources and labor in peripheral and semi-peripheral countries, thus establishing a cycle of dependency that inhibits these nations from achieving stable and significant economic growth. Dependency theory counters the perspective of modernization theory, which is criticized for its Eurocentric bias and suggests that development occurs through stages of industrialization and improved technology.