The sum of the angles will be a multiple of 180°. And in a polygon number of sides = number of angles.
If the first angle is 110, the others are consecutive : \(110-1,110-2,...\)
We have to make sure that their sum is a multiple of 180°. Let's try with A:
Tot sum angles: \(110+110-1+110-2+110-3+110-4=110*5-10=540\) multiple of 180. CORRECT
With every other option we would add one or more angles that would make the sum a "NOT" multiple of 180.
Example C) 7:\(110*7-1-2-3-4-5-6\) without doing any math here it's easy to see that \(-(1+2+3+4+5+6)=-21\) so their sum will not be a multiple of 180
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Kant , Critique of Pure Reason
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