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Question 136

If each interior angle of a regular polygon is $$135^\circ$$, then the number of sides of the polygon is

Solution

Each interior angle of the regular polygon = $$\frac{\left(n-2\right)180^{\circ\ }}{n}$$

Given, each interior angle of the regular polygon is $$135^\circ$$

$$\Rightarrow$$ $$\frac{\left(n-2\right)180^{\circ\ }}{n}=135^{\circ\ }$$

$$\Rightarrow$$ $$4\left(n-2\right)\ =3n$$

$$\Rightarrow$$ $$\ 4n-8=3n$$

$$\Rightarrow$$ $$n=8$$

$$\therefore\ $$Number of sides of the polygon = 8

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