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She deliberately broke the plate to show she was angry.
Literal
She [topic-は] angry [fact-こと] [object-を] show-let's [purpose-と] deliberately that plate [object-を] broke.
The volitional form 示そうと ('trying to show / in order to show') uses the volitional + と pattern expressing purpose. 怒っている事を示す = 'to show that she is angry,' with こと nominalizing the state of being angry. わざと ('deliberately') reinforces that this was intentional — a calculated display of anger through destruction.