Question

Tick (✓) the correct answer:
Each interior angle of a polygon is 135°. How many sides does it have?
(a) 8
(b) 7
(c) 6
(d) 10

Answer 1

(a) 8
​$$\begin{gathered} \mathrm{Each}\mathrm{interior}\mathrm{angle}\mathrm{of}\mathrm{a}\mathrm{regular}\mathrm{polygon}\mathrm{with}\mathrm{n}\mathrm{sides}=180-\left(\frac{360}{n}\right) \\ \Rightarrow 180-\left(\frac{360}{n}\right)=135 \\ \Rightarrow \frac{360}{n}=45 \\ \Rightarrow n=8 \end{gathered}$$