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UKMT Senior Mathematical Challenge, 2018

Geometry Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

How many pairs of numbers $(m,n)$ are there such that the following statement is true? 'A regular $m$ -sided polygon has an exterior angle of size $n°$ and a regular $n$ -sided polygon has an exterior angle of size $m°$ .'

(A) $24$ (B) $22$ (C) $20$ (D) $18$ (E) $16$

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