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# 4.How many sides does a regular polygon have if each of its interior angles is $$165^{\circ}$$?

Let the number of sides of a regular polygon be n.
We have, Sum of all interior angles = $$(n – 2) \times 180^{\circ}$$

and, measure of its each angle=$$\frac{(n-2) \times 180^{\circ}}{n}$$

here we have each angle as $$165^{\circ}$$

$$\Rightarrow \frac{(n-2) \times 180^{\circ}}{n}=165$$

$$\Rightarrow 180n - 360 =165 n \quad$$[Cross multiplication and opening the brackets]

$$\Rightarrow 180n -165 n=360$$

$$\Rightarrow 15n = 360$$

$$\Rightarrow n = \frac{360}{15}=24$$

So, we have the number of sides of regular polygon as 24.