How did Hawaii become a US territory or possession?

Answer 1

It could be argued that Hawai'i became a US possession in a less than above board manner.

The Kingdom of Hawai'i was illegally overthrown by The Committee of Safety (a group of wealthy American/European businessmen). The Committee of Safety used U.S. Marines to detain the Queen while they announced their takeover of Hawai'i.

The Queen's guard were ready to fight back (and easily outnumbered the marines), however, the Queen told her guard to stand down - saying that the U.S. would right this wrong.

U.S. President, Grover Cleveland actually attempted to restore governance to the Kingdom of Hawai'i, but lost his next election and was not able to see it through. His successor, William McKinley, saw Hawai'i as a valuable strategic military location.

This worked in favor of The Committee of Safety, as the had wanted Hawai'i to become a part of the U.S. in order to generate more revenue for their sugar trade (with the U.S.). With that said, The Committee of Safety handed Hawai'i over to the U.S. and was made a Territory.

These wealthy businessmen then began bringing in hundreds of thousands of immigrant workers (Chinese, Japanese, Filipino) to work their sugar plantations. Eventually, these immigrants became the majority - and by August 21, 1959, their overwhelming vote for Statehood made Hawai'i the 50th State.
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Answer 2

The United States and Great Britain interfered heavily in Hawaiian politics in the 1870s and 1880s. Two Hawaiian kings died without leaving heirs and this caused some political turmoil. Eventually a popular king (Kalakaua) was elected but a US-backed group forced him to sign a constitution reducing his authority.

That king died and his sister Liliʻuokalani became queen. The US interfered again and permitted a coup against her in 1893. A weak US-aligned republic was created and was annexed to the US in 1898. The Hawaiian leadership (all with Anglo-American names) agreed to the annexation. Hawaii entered the United States as a territory at that time.

Answer 3

By Act of Congress under the Newlands Resolution on 12 August of 1898.