How did Anne use humor to relieve the anxiety and boredom of living in hiding?
This is from the book questions “Anne Frank the diary of a young girl”

Anne uses sarcasm and humorous descriptions of her interactions especially with Mrs. van Daan.

Explanation:

At times, Anne uses humor as a way of dealing with the predicament she and her family are in. She especially uses sarcasm at times especially when she describes her interactions and clashes with her sister Margot. Anne mocks her sister in her diary and shows a bit of contempt how Margot is her mother's favorite. Anne has a lot of conflict with Mrs. van Daan or "Madame" as Anne calls her in her diary which in itself is tongue-in-cheek.  The moment in her diary where Mrs. van Daan is expressing one of her many opinions regarding Anne's personality and demeanor, Madame says that Anne should eat more vegetables. This was countered with a remark by Anne's father about Madame was now a pot calling the kettle black. Anne explained how this was funny because she knew it referred to how Madame is not able to eat cabbage and beans late at night otherwise she gets a lot of gas.  

where is the writing? (so i can answer)

honestly, is this even a but since you asked, he's probably at the store trying to get you food.