What does to be fed up mean?

[Nenad11]

English Language Tests, Intermediate level

ESL/EFL Test #347 "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 "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: 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?

[Beeesneees]

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.
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Cheers m' dears!