JAMB 1988 · UME · Q32

For which of the following exterior angles is a regular polygon possible? (i) $35^\circ$ (ii) $18^\circ$ (iii) $115^\circ$

Worked solution (try it first)

The exterior angles of a regular polygon are equal and add up to $360^\circ$ , so the number of sides is $360 \div (\text{exterior angle})$ , which must be a whole number.
$360 \div 35 \approx 10.3$ and $360 \div 115 \approx 3.1$ : neither is whole.
$360 \div 18 = 20$ , a polygon with 20 sides.
So only (ii) works, option B.