JAMB 1989 · UME · Q33

A regular polygon of $(2k + 1)$ sides has $140^\circ$ as the size of each interior angle. Find $k$ .

Worked solution (try it first)

Each exterior angle is $180^\circ - 140^\circ = 40^\circ$ , so the polygon has $360 \div 40 = 9$ sides.
So $2k + 1 = 9$ .
Subtract 1: $2k = 8$ .
Divide by 2: $k = 4$ , option A.