Why so much federally owned land?

Can someone answer the question, how did the federal government get to be in charge of over 80 percent of the state of Nevada? And large percentages of other Western states? Constitutionally, how is that possible?

If I'm understanding it right, the federal government was given 10 square miles of land to build a capital, which is now known as Washington, D.C. And all land within a state's border belongs to the state, unless the federal government purchases land from the state, with the approval of the state legislature, for federal buildings or military bases.

So, are we to think that the federal government bought all that land from the state of Nevada? And what about other Western states that have a large federal "ownership"? How did all this happen, especially when you look at the older states where the federal government owns very little.

Recently, representatives from several Western states met to discuss this very issue. I just happened to see it on an online news organization. Never heard it on any mainstream news media. And now the BLM is attempting to steal land from Texas along the Red River. Don't mess with Texas!

Al Haak

Palatine