"To the extent that"

1.To the extent that he felt the world was unjust or unfair, that bothered him. 2. To the extent that the federal government didn’t do it’s job right, I take responsibility. What does this phrase “to the extent that” really mean and how it connects to the main clause. Please explain with regards to it’s literal connection to the sentence. Thanks in advance.

Those examples (particularly the first)don’t seem to be particularly good or useful. I recognise the 2nd as something from President Bush. He was saying that he takes responsibility for the things that the federal government didn’t do right.

It means something along the lines of ‘in view of the fact that…’/ ‘given the fact that’ and simplistically could be considered in most instances to mean something similar to ‘since’ (though I would not advocate the actual replacement of the phrase with the word ‘since’).

‘To the extent’ can be followed by other prepositions which change the meaning slightly. Here’s an example:
He said he didn’t like President Bush, but not to the extent of wanting to kill him.
‘To the extent of…’ - to the point of / to the level of