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Answer :
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.