WAEC Mathematics

Each interior angle of a regular polygon is 168°. Find the number of sides of the polygon.

a.

30

b.

36

c.

24

d.

18

Correct answer: A

Each of the interior angles of an n-sided regular polygon is given by the formula $\theta = \frac{(n-2)\times180}{n}$. We are told that each of the interior angles of a regular polygon is $168°$. This means that $168 = \frac{(n-2)\times180}{n}$.

So $168n = (n-2) \times 180$, $168n = 180n - 360$, $360 = 12n$, $n = \frac{360}{12}$, $n = 30$