The quality or state of being annoying; how much something irritates or bothers people.
From 'annoying' (present participle of 'annoy') plus '-ness' (state or quality), showing how English builds abstract nouns from adjectives.
If you had to measure how much your sibling annoyed you, you'd be measuring 'annoyingness'—it's a real word for a feeling everyone knows but few bother to name.
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