U.S. Geography: What is the eastern most state and what is the western most state?

Maine and Alaska.

https://en.wikipedia.org/wiki/List_of_extreme_points_of_the_United_States

FYI, Alaska also has the northernmost, while Florida has southernmost (the Keys)

Some say that Alaska is both the eastern most state of the USA and western most state of the USA, as it's all a matter of definition [ east = eastern hemisphere and west = western hemisphere]:

... Alaska's Aleutian Islands stretch right up to the edge of the Western Hemisphere at the 180º line of Longitude, thus the most western state in the country. Alaska is also the answer for eastern, as the Aleutian Islands stretch across the 180º line of Longitude, into the Eastern Hemisphere, and up the edge of the Russian Federation ... Pochnoi Point, Semisopochnoi Island, Alaska 51°57'42"N 179°46'23"E Amatignak Island, Alaska 51°16'7"N 179°8'55"W Thereby making the point in the U.S. that is the farthest east Pochnoi Point and the point in the U.S. that is farthest west Amatignak Island ...

If the question is, "What is the farthest point east and what is the farthest point west in the U.S.?", then Alaska is the answer. It contains the point with the westernmost longitude and it contains the point with the easternmost longitude. The ambiguity arises when the question asked is, "What is the easternmost state and what is the westernmost state in the U.S.?" This is because there are at least three different definitions of "easternmost" and "westernmost".

https://travel.stackexchange.com/questions/6070/ive-been-told-one-state-in-the-us-is-the-easternmost-westernmost-and-northernm

Arguably, Alaska is both the easternmost and westernmost state. Semisopochnoi Island is just west of the 180° meridian at 179°46' E.
From the link provided above and this one, which comes from it, https://en.wikipedia.org/wiki/Semisopochnoi_Island

Also, Hawaii (which has a latitude range of 18°?55? N to 28°?27? N) has parts which are further south than Florida (with a latitude range of 24° 27' N to 31° 00' N).

https://en.wikipedia.org/wiki/Hawaii

https://en.wikipedia.org/wiki/Florida

I won't argue with Alaska being the northernmost state!

According to the Wikipedia article cited in the first answer, Alaska is both the Easternmost and the Westernmost, as well as being the Northernmost.

Pochnoi Point, Semisopochnoi Island, Alaska 51°57?42?N 179°46?23?E - easternmost point in all U.S. territory by longitude

https://en.wikipedia.org/wiki/List_of_extreme_points_of_the_United_States

The southernmost, from the same source, is in Hawaii. The keys are the southernmost of the 48 'contiguous' states.

Ka Lae, Hawaii (18°54?39?N 155°40?52?W) - southernmost point in the 50 states

The easternmost state is Maine at the West Quoddy Head lighthouse (66 degrees 57 minutes west).
The northernmost state is Alaska at Point Barrow (71 degrees 23 minutes north).
The westernmost state is also Alaska at Cape Wrangell on Attu Island (172 degrees 27 minutes east).
The southernmost state is Hawaii at Ka Lae (18 degrees 55 minutes north).

https://www.thoughtco.com/states-farthest-north-south-east-west-4071599

In my first answer, I was merely addressing it as an overhead view of the USA. The rightmost (eastern) is Maine. Yes, Due to the Int'l Date line, Alaska can also be the easternmost. Technically its Alaska. Overhead view, its Maine. So, it depends on what you are after in the question.