in which industry did women find increased opportunities for employment during the early 1800s?

Women found employment opportunities mainly in the textile industry.

Explanation:

During the Industrial Revolution many women began to have opportunities to work in the new factories.  One of the biggest industries that often hired women and children was the textile industry.  Women would work operating machines such as the cotton mill, the power loom, the spinning mule or the flying shuttle.

One reason why factories hired women was because they were paid lower wages than men.