WAEC 2008 · Paper 2 · Q2✱

(b)
Each interior angle of a regular polygon is $(134 + n)^\circ$ , where $n$ is the number of sides. Find $n$ .
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

Each exterior angle is $180^\circ - (134 + n)^\circ = (46 - n)^\circ$ .
The exterior angles of any polygon add up to $360^\circ$ , and here there are $n$ equal ones: $n(46 - n) = 360$ .
Expand and rearrange: $n^2 - 46n + 360 = 0$ .
Factorise: $(n - 10)(n - 36) = 0$ , so $n = 10$ or $n = 36$ .
Both work: a 10-sided polygon has interior angles of $144^\circ$ ( $= 134 + 10$ ) and a 36-sided one has $170^\circ$ ( $= 134 + 36$ ).
So $n = 10$ or $36$ .