What does clause cross to bear mean?

English Language Tests, Intermediate level

ESL/EFL Test #327 [color=blue]“English Slang Idioms (48)”, question 3

“My brother always shows up out of the blue and expects me to give him a place to stay and food to eat. It’s very annoying, but I guess that’s just my to bear,” Ella said to Grace.

(a) cross
(b) trial
(c) crime
(d) load

English Language Tests, Intermediate level

ESL/EFL Test #327 [color=blue]“English Slang Idioms (48)”, answer 3

“My brother always shows up out of the blue and expects me to give him a place to stay and food to eat. It’s very annoying, but I guess that’s just my cross to bear,” Ella said to Grace.

Correct answer: (a) cross

Your answer was: [color=red]incorrect
“My brother always shows up out of the blue and expects me to give him a place to stay and food to eat. It’s very annoying, but I guess that’s just my load to bear,” Ella said to Grace.
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Does clause cross to bear mean something which is meant to be the way it is,something which is one’s destiny?

Yes, it’s a burden/responsibility/obligation that you just have to live or deal with.

In Hungary say: Everybody bears his own cross.