The quality or state of being angular; the characteristic of having sharp corners, distinct edges, or awkward angles.
From 'angular' plus the suffix '-ness' meaning state or quality. The base word 'angular' comes from Latin 'angulus' (corner), so 'angulateness' literally means 'the quality of having corners.'
'Angulateness' is a word that's technically perfect but almost never used—if you wanted to describe why someone's face looks sharp and defined, you'd probably just say 'angular features' instead of calling it 'angulateness,' which shows how word formation rules and actual usage sometimes diverge!
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