What does to be fed up mean?

English as a Second Language English Teacher Explanations (ESL Tests)
1

English Language Tests, Intermediate level

ESL/EFL Test #347 [color=blue]“English Slang Idioms (68)”, question 9

“If the landlord doesn’t fix our plumbing soon, I am going to report him to the city. I am fed up to the … teeth with how long it takes him to fix things around here,” Beth said to Mike.

(a) front
(b) buck
(c) sharp
(d) back

English Language Tests, Intermediate level

ESL/EFL Test #347 [color=blue]“English Slang Idioms (68)”, answer 9

“If the landlord doesn’t fix our plumbing soon, I am going to report him to the city. I am fed up to the back teeth with how long it takes him to fix things around here,” Beth said to Mike.

Correct answer: (d) back

Your answer was: [color=red]incorrect
“If the landlord doesn’t fix our plumbing soon, I am going to report him to the city. I am fed up to the buck teeth with how long it takes him to fix things around here,” Beth said to Mike.
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Does to be fed up to the back teeth mean that all the limits crosses the red line of smb’s patience so one becomes anger,furious?

2

It simply means to be intensely annoyed or upset about something.

If it were possible for a human being to literally be fed up to the back teeth, it would mean that your food filled your stomach, oesophagus and throat right up to your mouth cavity.