Question

Tick (✓) the correct answer:
The interior angle of a regular polygon exceeds its exterior angle by 108°. How many sides does the polygon have?
(a) 16
(b) 14
(c) 12
(d) 10

Answer 1

(d) 10

​$$\begin{gathered} \mathrm{Each}\mathrm{exterior}\mathrm{angle}\mathrm{of}\mathrm{a}\mathrm{regular}\mathrm{polygon}=\frac{360}{n} \\ \mathrm{Each}\mathrm{interior}\mathrm{angle}\mathrm{of}\mathrm{a}\mathrm{regular}\mathrm{polygon}=180-\frac{360}{n} \\ 180-\frac{360}{n}-108=\frac{360}{n} \\ \frac{720}{n}=180-108=72 \\ n=\frac{720}{72}=10 \end{gathered}$$